Fully-characteristic subgroup
From Encyclopedia of Mathematics
A subgroup of a group 
that is invariant with respect to all endomorphisms of 
. The set of fully-characteristic subgroups forms a sublattice in the lattice of all subgroups. The commutator subgroup and the members of the lower central series in an arbitrary group are fully-characteristic subgroups. In addition, any verbal subgroup of a group is fully characteristic. The converse statement is true for free groups: Any fully-characteristic subgroup is verbal.
References
| [1] | W. Magnus, A. Karrass, B. Solitar, "Combinatorial group theory: presentations of groups in terms of generators and relations" , Interscience (1966) |
How to Cite This Entry:
Fully-characteristic subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fully-characteristic_subgroup&oldid=13679
Fully-characteristic subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fully-characteristic_subgroup&oldid=13679
This article was adapted from an original article by V.N. Remeslennikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article