# Characteristic subgroup

From Encyclopedia of Mathematics

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

#### Comments

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: http://encyclopediaofmath.org/index.php?title=Characteristic_subgroup&oldid=15360

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article