...
order other than the unit element (see [[
Order|
Order]] of an element of a
group).
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> A.G. Kurosh, "The
theory of groups" , '''1–2''' , Chelsea (1955–1956) (Translated from Russian
424 bytes (63 words) - 17:29, 7 February 2011
''dihedron group''
...In a finite group, two different elements of order 2 generate a dihedral group.
1 KB (202 words) - 16:24, 19 October 2014
''Hamiltonian group''
...rticular, any Hamiltonian group is periodic (cf. [[Periodic group|Periodic group]]).
928 bytes (136 words) - 17:28, 7 February 2011
...umber) is metacyclic. Polycyclic groups (cf. [[Polycyclic group|Polycyclic group]]) are a generalization of metacyclic groups.
...the more special class of groups whose derived group and derived quotient group are both cyclic.
709 bytes (107 words) - 17:03, 7 February 2011
...cept $n=4$, this group is simple; this fact plays an important role in the theory of solvability of algebraic equations by radicals.
Note that $A_5$ is the non-Abelian simple group of smallest possible order.
951 bytes (151 words) - 19:22, 4 April 2023
''torsion-free group''
...with respect to two different prime numbers $p$, then it is a torsion-free group.
1 KB (176 words) - 11:51, 26 April 2014
...rder 8 is the smallest finite group that is not a T-group. A group is a T-group if and only if it is equal to its own [[Wielandt subgroup]].
* Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) {{ISBN|0
653 bytes (107 words) - 20:32, 18 November 2023
...e of subgroups of a group is a [[distributive lattice]] if and only if the group is locally cyclic.
* Marshall Hall jr, ''The Theory of Groups'', reprinted American Mathematical Society (1976)[1959] {{ISBN|0-
667 bytes (99 words) - 20:32, 18 November 2023
''equi-affine group''
The subgroup of the general [[affine group]] consisting of the affine transformations of the $n$-dimensional affine sp
1 KB (158 words) - 22:38, 2 November 2014
...up, proved by L. Sylow [[#References|[1]]] and playing a major role in the theory of finite groups. Sometimes the union of all three theorems is called Sylow
Let $G$ be a finite group of order $p^ms$, where $p$ is a prime number not dividing $s$. Then the following th
2 KB (372 words) - 19:17, 4 April 2023
...$ and its centralizer $K$ in $G$; indeed $K$ is isomorphic to the quotient group $G/B$.
...form space]] with respect to the [[uniformity]] implied by the topological group structure.
1 KB (238 words) - 15:02, 19 November 2023
$#C+1 = 31 : ~/encyclopedia/old_files/data/P071/P.0701710 Partially ordered group
A [[Group|group]] $ G $
2 KB (362 words) - 08:05, 6 June 2020
''cyclic semi-group''
...le$, then $a,\dots,a^{h+d-1}$ are distinct elements and, consequently, the order of $A$ is $h+d-1$; the set
2 KB (405 words) - 19:33, 21 November 2014
''soluble group''
...] of a group). The term "solvable group" arose in [[Galois theory|Galois theory]] in connection with the solvability of algebraic equations by radicals.
3 KB (443 words) - 18:25, 26 October 2014
...gebras was discovered by C. Chevalley [[#References|[2]]] (cf. [[Chevalley group]]). In particular, Chevalley's method makes it possible to obtain Dickson g
[[Category:Group theory and generalizations]]
1 KB (187 words) - 21:05, 15 November 2017
...Every pure linear sub-semi-group $P$ of an arbitrary group defines a right order, namely $x<y$ if and only if $yx^{-1}\in P$.
...ll subgroups in $S(G)$ become convex. In a locally nilpotent right-ordered group the system of convex subgroups is solvable.
4 KB (585 words) - 06:17, 28 March 2023
...r groups are said to be cyclic (they are isomorphic to either the additive group $\mathbf Z$ of integers, or the additive groups $\mathbf Z_n$ of residue cl
...groups that are simple (cf. [[Finitely-presented group|Finitely-presented group]]).
2 KB (343 words) - 18:24, 26 October 2014
A metabelian $2$-group (cf. [[Meta-Abelian group|Meta-Abelian group]]) of order 8, defined by generators $x,y$ and relations
The quaternion group can be isomorphically imbedded in the multiplicative group of the algebra of quaternions (cf. [[Quaternion|Quaternion]]; the imbedding
2 KB (350 words) - 14:38, 2 August 2014
''$p$-component of a group element of finite order''
...or $p$-component of $x$ and $z$ is the $p'$-part or $p'$-component. If the order of $x$ is $r=p^{\alpha}s$, $(p,s)=1$, $bp^{\alpha}+cs=1$, then $y=x^{sc}$,
1 KB (201 words) - 20:11, 25 March 2024
A [[P-group| $ p $-
group]] $ G $
2 KB (283 words) - 08:10, 6 June 2020
[[Semi-group|semi-group]]. In particular, if $S$ is a group, one obtains a
...p $S$ is semi-simple if and only if all linear representations of the semi-group $S$ over the algebra $\Phi$ are reducible.
2 KB (344 words) - 19:41, 8 December 2015
...7 : ~/encyclopedia/old_files/data/P071/P.0701010 \BMI \Gpi\EMI\AAhsolvable group
A generalization of the concept of a [[Solvable group|solvable group]]. Let $ \pi $
3 KB (420 words) - 08:06, 6 June 2020
A ''torsion group'' (also called ''periodic group'')
[[Group|group]] in which every element has finite order. Any torsion
1 KB (170 words) - 21:20, 29 April 2012
...on, that is, it can be imbedded in a unique locally nilpotent torsion-free group $G^*$ such that all equations of the form $x^n=g$ are solvable in $G^*$, wh
<TR><TD valign="top">[1]</TD> <TD valign="top"> A.G. Kurosh, "The theory of groups" , '''1–2''' , Chelsea (1955–1956) (Translated from Russian
1 KB (227 words) - 18:28, 5 April 2018
...://www.encyclopediaofmath.org/legacyimages/c/c110/c110400/c1104002.png" />-
group]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org
...ges/c/c110/c110400/c11040010.png" /> is partially ordered with the induced
order: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/
15 KB (2,061 words) - 17:13, 7 February 2011
''totally ordered group''
A [[Po-group| $ po $-
4 KB (587 words) - 08:03, 6 June 2020
...eal numbers in the interval $(0,1)$ and the symbol $\infty$ with the usual order and with the operations:
The former case occurs if and only if $S$ is a [[semi-group with cancellation]].
3 KB (413 words) - 09:17, 2 April 2023
...egacyimages/h/h110/h110290/h11029025.png" />, which is identified with the
group of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.or
....encyclopediaofmath.org/legacyimages/h/h110/h110290/h11029051.png" />-Hopf
order in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.or
13 KB (1,801 words) - 19:17, 12 January 2018
...rs from the theory of groups (i.e. $2$-groups). Thus, if $n\geq 3$, an $n$-group has no analogue of the unit element.
Let $\Gamma(\circ)$ be a group with multiplication operation $\circ$; let $n\geq 3$ be an arbitrary intege
2 KB (307 words) - 21:09, 21 November 2014
...with the operation of multiplication in the skew-field. The multiplicative group of a field is Abelian.
...lic group or is a finitely-solvable group and has an extension to a linear group over a skew-field. Some cases are known, e.g., [[#References|[a2]]].
1 KB (219 words) - 20:48, 21 December 2014
''in a group $G$''
...he order of a subgroup $H$ by its index $\left|G:H\right|$ is equal to the order of $G$ (Lagrange's theorem). This relationship applies to finite groups $G$
1 KB (186 words) - 11:18, 20 April 2012
...ng all elements of the groupoid (in any order); these symbols (in the same order) are also listed in front of the first column. If the groupoid has an ident
Cayley tables were first used by A. Cayley in 1854 for groups (cf. [[Group|Group]]).
2 KB (300 words) - 16:43, 4 June 2020
''of a finite group $ G $''
see [[Sylow subgroup|Sylow subgroup]]). A group $ G $
2 KB (376 words) - 08:03, 6 June 2020
be a [[Finite group|finite group]] and $ \pi $
a subset of the prime numbers that divide the order $ n $
2 KB (287 words) - 08:24, 6 June 2020
$#C+1 = 18 : ~/encyclopedia/old_files/data/P074/P.0704570 Primitive group of permutations,
''primitive permutation group''
3 KB (484 words) - 08:07, 6 June 2020
...g/legacyimages/f/f120/f120130/f1201301.png" /> denote an arbitrary [[
Group|
group]] (finite or infinite) and let <img align="absmiddle" border="0" src="https
...opediaofmath.org/legacyimages/f/f120/f120130/f12013038.png" /> is a finite
group, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/
16 KB (2,143 words) - 17:10, 7 February 2011
The ''complexification of a Lie group $G$ over $\R$'' is
a complex Lie group $G_\C$ containing $G$ as a real Lie subgroup such that the Lie algebra $\de
3 KB (501 words) - 15:05, 13 April 2024
''right-ordered group''
A [[Group|group]] $ G $
4 KB (580 words) - 06:18, 28 March 2023
...n group theory. Most are not intrinsic to a group itself, but pertain to a group acting on something.
==Regular group of permutations.==
4 KB (716 words) - 07:52, 25 November 2023
$#C+1 = 13 : ~/encyclopedia/old_files/data/L058/L.0508600 Lie group, Banach
endowed with a group structure and an analytic Banach manifold structure (cf. [[Banach analytic
3 KB (427 words) - 22:16, 5 June 2020
The [[Exponent of a group|exponent]] of the multiplicative group of integers modulo $n$, denoted $\lambda(n)$; the least positive integer $\
Since the multiplicative group modulo an odd prime power $p^a$ is cyclic, in these cases we have $\lambda(
1 KB (186 words) - 16:57, 25 November 2023
...ad. A Baer group is maximal of elation, respectively homology, type if the group acts transitively on the non-fixed points on each line $L$ of the spread wh
...gn="top">[a2]</TD> <TD valign="top"> V. Jha, N.L. Johnson, "Structure theory for point-Baer and line-Baer collineation groups in affine planes" , ''Proc
2 KB (305 words) - 17:24, 2 September 2017
A norm on a skew-field the group of values of which is isomorphic to the group of integers $ \mathbf Z $.
is also sometimes understood as the norm having as group of values the $ r $-
1 KB (165 words) - 19:36, 5 June 2020
...cally finite group]]), finiteness of rank (cf. [[Rank of a group|Rank of a group]]), and finiteness of conjugacy classes (cf. [[Conjugate elements|Conjugate
...t groups (cf. [[Nilpotent group|Nilpotent group]]) it is equivalent to the group itself being finitely generated.
5 KB (720 words) - 17:15, 7 February 2011
...subgroups are conjugate in $G$. Any $\pi_1$-subgroup of a $\pi$-separable group $G$ is contained in some $\pi_1$-Hall subgroup of $G$ (see [[#References|[2
...and if all prime divisors of $k$ are in $\pi$, then $G$ has a subgroup of order $k$ and all these subgroups are conjugate in $G$. If $\pi$ consists of all
2 KB (379 words) - 09:33, 27 October 2014
...23 : ~/encyclopedia/old_files/data/M064/M.0604790 Monomial substitutions, group of
The subgroup of the group $ \mathop{\rm GL} ( m , \mathbf Z [ H ] ) $
2 KB (302 words) - 08:01, 6 June 2020
...ollowing generalization of Frobenius' theorem: If $G$ is a finite group of order $g$ and $C$ is a [[conjugacy class]] of $G$ of cardinality $h$, then the nu
...mple, $x^4=1$ has exactly $4$ solutions in the [[Symmetric group|symmetric group]] on three letters, but obviously the solutions do not form a subgroup of $
4 KB (650 words) - 20:59, 29 November 2014
...on, a [[Totally ordered set|totally ordered set]] with respect to a binary order relation $\leq$ and satisfies the following axiom: For any elements $x,y,z\
...$ satisfying conditions 1)–4), then $G$ can be made into a totally ordered group with $P$ as set of positive elements.
3 KB (495 words) - 19:18, 17 August 2014
...e group generated by all right translations of a finite distributive quasi-group is solvable [[#References|[4]]].
...ign="top">[3]</TD> <TD valign="top"> V.D. Belousov, "Foundations of the theory of quasi-groups and loops" , Moscow (1967) (In Russian)</TD></TR>
3 KB (425 words) - 22:16, 7 January 2017
...oup algebra]]; [[Cross product|Cross product]]), with $|G|=q$. An $R$-Hopf order in $KG$ is a rank-$q$ $R$-Hopf algebra $H$ (cf. [[Hopf algebra|Hopf algebra
...(g)$. Then the $R$-Hopf order in $KG$ determined by $\xi$ (called a Larson order) is of the form
5 KB (919 words) - 04:20, 15 February 2024
...|nil semi-group]], or $S$ is a subdirect product of a group and a nil semi-group.
...nown (including necessary and sufficient ones) under which a periodic semi-group is a band of torsion classes; this clearly occurs for commutative semi-grou
5 KB (775 words) - 17:22, 17 October 2014
...lity in the lattice of all subgroups of a finite group (cf [[Supersolvable group]]).
<TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Hall, Jr., "The theory of groups" , Macmillan (1964) {{ZBL|0116.25403}}</TD></TR>
779 bytes (109 words) - 19:05, 1 May 2024
''Černikov group''
...also Chernikov; further, an extension of a Chernikov group by a Chernikov group is again Chernikov.
4 KB (589 words) - 18:19, 15 January 2017
''group algebra of a group $G$ over a field $K$''
...a; multiplication of basis elements in the group algebra is induced by the group multiplication. The algebra $KG$ is isomorphic to the algebra of functions
5 KB (872 words) - 22:00, 29 April 2012
A matrix group $G$ over an arbitrary fixed field $K$, all elements of which may be reduced
...mpletely reducible. Every normal subgroup of a completely-reducible matrix group is itself completely reducible.
2 KB (303 words) - 16:55, 10 April 2016
...e poly-nilpotent length is less than the solvable length. A poly-nilpotent group of length 2 is called meta-nilpotent.
...ncreasing) poly-nilpotent series of length $l$ whose factors in increasing order have nilpotent classes not exceeding the numbers $c_1,\dots,c_l$, respectiv
2 KB (229 words) - 16:12, 4 October 2014
The automorphism group of a
group of all automorphisms of the field $L$ leaving the elements of
3 KB (494 words) - 21:56, 5 March 2012
$#C+1 = 10 : ~/encyclopedia/old_files/data/S084/S.0804920 Shmidt group
...lpotent group]]). A Shmidt group is a [[Solvable group|solvable group]] of order $ p ^ \alpha q ^ \beta $,
2 KB (346 words) - 18:45, 11 April 2023
...G. Fubini in 1916 (a generalization of this concept to the geometry of any group of transformations was obtained by E. Cartan in 1920) using the concept of
be the group of transformations of a space $ E $.
3 KB (529 words) - 08:08, 6 June 2020
A group having a [[Normal series|normal series]]
...group itself), and their lengths are equal to the nilpotency class of the group.
3 KB (500 words) - 16:51, 30 December 2018
''(in group theory)''
rank of a [[Finite group|finite group]] $ G $
4 KB (568 words) - 14:10, 31 December 2020
...dered set]], a subset which is totally ordered with respect to the induced order. The [[rank of a partially ordered set]] is the maximal cardinality of a c
...a group $G$ is an element of the tensor product of a chain complex by the group $G$.
1 KB (171 words) - 15:33, 18 March 2023
''idempotent semi-group''
...study of many properties of idempotent semi-groups. Every idempotent semi-group is locally finite.
4 KB (534 words) - 16:11, 12 April 2014
A group of observations in a sample that have the same value. Let $ X _ {1} \dots
of the order statistics (cf. [[Order statistic|Order statistic]])
4 KB (604 words) - 08:25, 6 June 2020
''of an Abelian group or semigroup $M$''
...rac27 n$. The set of odd numbers in $\{1,\ldots,n\}$ is a sum-free set of order $\frac12 n$.
660 bytes (110 words) - 16:47, 23 November 2023
...a so-called Frobenius complement in $G$; the group $G$ is then a Frobenius group by definition. It was proved by G. Frobenius in 1901, see [[#References|[a3
...$ is a subgroup of $G$ is still the only existing proof; it uses character theory! The normal subgroup $N$ is called the Frobenius kernel of $G$.
9 KB (1,463 words) - 07:41, 27 January 2024
$#C+1 = 182 : ~/encyclopedia/old_files/data/O070/O.0700040 Order
The order of an algebraic curve $ F ( x , y ) = 0 $,
13 KB (2,001 words) - 02:12, 1 March 2022
$#C+1 = 80 : ~/encyclopedia/old_files/data/L057/L.0507670 Lattice\AAhordered group,
'' $ l $-group''
5 KB (738 words) - 08:45, 8 October 2023
of a group $ G $
is said to be a coset of the group $ G $
2 KB (298 words) - 19:36, 5 June 2020
...in the [[Group algebra|group algebra]] $F G$ of some [[Finite group|finite group]] $G$. Since the Schur indices for $G$ are trivial in prime characteristic
...is group]]), in the sense of E. Noether, where the factor sets have finite order.
4 KB (692 words) - 17:46, 1 July 2020
...ension $K/k$ is isomorphic to the $p$-adic Lie group $\mathbb{Z}_{p}$, the group of $p$-adic integers.
...e. These results have been applied in algebraic number theory and in group theory.
2 KB (327 words) - 11:17, 9 April 2023
...tiplicative group]] of residue classes modulo $p$ divides the order of the group. Fermat's little theorem was generalized by L. Euler to the case modulo an
...n="top">[1]</TD> <TD valign="top"> I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian)</TD></TR></table>
2 KB (257 words) - 18:02, 8 November 2014
...-group $S$ is a [[total order]], then $S$ is called a totally ordered semi-group (cf. also [[Totally ordered set]]). If the relation $\le$ on $S$ defines a
..., is a variety (cf. also [[Variety of groups]]). On a lattice-ordered semi-group the identities
11 KB (1,676 words) - 14:07, 17 March 2020
...al order on the set $E$ of idempotent elements, called the natural partial order on $E$. Two idempotents $u$ and $v$ of a ring are said to be orthogonal if
...ing as an idempotent element of the semi-group of unary operations. In the theory of $R$-modules, the affine operations are those of the form
1 KB (226 words) - 12:30, 14 February 2020
...d $k$ with given [[Galois group|Galois group]] (cf. [[Galois theory|Galois theory]]), and of stating the conditions which ensure the existence (and non-exist
...comes down to finding an algebraic equation over $k$ with the given Galois group. Such equations exist for the symmetric groups, and also for the alternatin
4 KB (586 words) - 04:07, 25 February 2022
...d by identifying the elements of the block design with the elements of the group and the blocks with the sets $\{d_1g,\dots,d_kg\}$, where $g$ runs over $G$
...tiplier of a difference set turns out to be useful: An automorphism of the group $G$ is a multiplier of a $(v,k,\lambda)$-difference set $D$ in $G$ if it is
5 KB (832 words) - 10:37, 15 November 2014
''lattice-ordered group''
A partially ordered group $ \{ G; \cdot, \cle \} $(
9 KB (1,403 words) - 22:15, 5 June 2020
...ound in many textbooks on combinatorics and many elementary books on group theory (see, for example, [[#References|[a5]]], Chap. 9).
.... There are several lemmas and theorems in group theory and representation theory to which the name of William Burnside is correctly attached (for example: B
3 KB (516 words) - 22:29, 1 December 2014
$#C+1 = 37 : ~/encyclopedia/old_files/data/W097/W.0907770 Whitehead group
An Abelian group associated with an associative ring in the following manner. It was introdu
4 KB (564 words) - 08:29, 6 June 2020
$#C+1 = 51 : ~/encyclopedia/old_files/data/M110/M.1100180 Modular group algebra
a [[Group|group]]. The [[Group algebra|group algebra]] $ FG $
5 KB (726 words) - 08:01, 6 June 2020
$#C+1 = 51 : ~/encyclopedia/old_files/data/F040/F.0400290 Finite group scheme
A group scheme that is finite and flat over the ground scheme. If $ G $
5 KB (753 words) - 09:02, 8 April 2023
The notion of a ''group scheme'' is a generalization of the concept of an
[[Algebraic group|algebraic group]]. Let ${\rm Sch}/S$ be the category of
5 KB (831 words) - 21:59, 5 March 2012
...le p,+\rangle$ can be turned into a [[partially ordered set]] (the partial order $\leq$ is defined by the relation $a\leq b$ if and only if $a+b=b$) in whic
...ent (cf. also [[Band of semi-groups]]) (which is a decomposition of a semi-group into sub-semi-groups forming a band). Thus, an upper (lower) semi-lattice d
2 KB (272 words) - 12:05, 23 November 2023
$#C+1 = 112 : ~/encyclopedia/old_files/data/F040/F.0400280 Finite group, representation of a
A homomorphism of a finite group $ G $
10 KB (1,488 words) - 19:39, 5 June 2020
...$K / k$ that leave all elements of $k$ invariant is called the ''[[Galois group]]'' of
...rm{Gal}}\Gal(K/k)$. The study of these groups is a major part of [[Galois theory]].
2 KB (423 words) - 13:52, 25 November 2023
A group $G$ provided with the structure of an
mappings (morphisms) of algebraic varieties. An algebraic group is
4 KB (665 words) - 18:32, 10 December 2015
cf. [[Geometric objects, theory of|Geometric objects, theory of]]) be given in a differentiable manifold $ X _ {n} $,
of this manifold is known as a differential invariant of order $ r $
5 KB (725 words) - 19:35, 5 June 2020
is the structure Lie group of the principal bundle $ ( X , p , M ^ {n} ) $
or, in another terminology, the representation space of the Lie group $ \mathfrak G $.
6 KB (860 words) - 17:33, 5 June 2020
...cending and descending chains of normal subgroups have finite length. If a group has two principal series, then they are isomorphic, i.e. they have the same
...</TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Hall jr., "The theory of groups" , Macmillan (1959) pp. 124</TD></TR><TR><TD valign="top">[a3]<
2 KB (254 words) - 16:51, 30 December 2018
from an (Abelian) [[Semi-group|semi-group]] $ H $
to subsets of an (Abelian) semi-group $ G $
2 KB (318 words) - 16:09, 1 April 2020
be a [[Group|group]] of order $ v $
difference set of order $ n = k - \lambda $
5 KB (803 words) - 06:20, 26 March 2023
be a [[Finite group|finite group]], $ K $
is a splitting field for a finite group $ G $
3 KB (533 words) - 08:12, 6 June 2020
...logical group with respect to this topology and therefore is not a compact group.
...$ \mathbf R $ , respectively) and, more generally, any compact real Lie group.
8 KB (1,117 words) - 20:03, 27 February 2021
...a [[Galois extension|Galois extension]] of $\mathbf Q$ with a given finite group $G$ (see [[#References|[5]]]). The problem is also closely connected with t
...of $K^G$ in the case of an Abelian group $G$ is closely connected with the theory of algebraic tori (cf. [[Algebraic torus|Algebraic torus]]) (see [[#Referen
4 KB (603 words) - 17:59, 23 November 2014
...lement $\zeta$ generates the [[cyclic group]] $\mu_m$ of roots of unity of order $m$.
...t $\zeta^k$ is also a primitive root. The number of all primitive roots of order $m$ is equal to the value of the [[Euler function]] $\phi(m)$ if $\mathrm{h
3 KB (496 words) - 07:46, 20 December 2014
A [[Semi-group|semi-group]] in which every element is regular (see [[Regular element|Regular element]
An arbitrary regular semi-group $ S $
10 KB (1,515 words) - 08:10, 6 June 2020
...rak{gl}(V)$ is naturally identified with the set of all square matrices of order $n$ over $K$ and is denoted by $\mathfrak{gl}(n,K)$. Any linear Lie algebra
...he Lie algebra of the analytic group $G$ (cf. [[Lie algebra of an analytic group]]) is naturally identified with a Lie subalgebra of $\mathfrak{gl}(V)$, tha
3 KB (554 words) - 19:21, 24 February 2017
group $ K _ {2} ( {\mathcal O} _ {F} ) $,
is an [[Abelian group|Abelian group]] of finite order.
5 KB (731 words) - 08:21, 26 March 2023
''inverse semi-group''
...nverse semi-group [[#References|[7]]]. Every congruence on an inverse semi-group is determined by the classes containing idempotents.
7 KB (986 words) - 19:33, 2 January 2018
$#C+1 = 56 : ~/encyclopedia/old_files/data/P075/P.0705050 Profinite group
A topological group that is the [[Projective limit|projective limit]] of an inverse system of f
5 KB (778 words) - 19:48, 21 January 2021