Cyclic group
From Encyclopedia of Mathematics
A group with a single generator. All cyclic groups are Abelian. Every finite group of prime order is cyclic. For every finite number 
there is one and, up to isomorphism, only one cyclic group of order 
; there is also one infinite cyclic group, which is isomorphic to the additive group 
of integers. A finite cyclic group 
of order 
is isomorphic to the additive group of the ring of residues 
modulo 
(and also to the group 
of (complex) 
-th roots of unity). Every element 
of order 
can be taken as a generator of this group. Then
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How to Cite This Entry:
Cyclic group. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cyclic_group&oldid=13750
Cyclic group. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cyclic_group&oldid=13750
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098