Characteristic subgroup

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A subgroup of a group that is invariant under all automorphisms of .


Examples of characteristic subgroups are the centre of a group, denoted by , the Fitting subgroup, , the commutator subgroup, , or , the Frattini subgroup, , the socle, , the layer, , and the generalized Fitting subgroup. For a definition of the last two, cf. Fitting subgroup.

How to Cite This Entry:
Characteristic subgroup. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article