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.
Characteristic subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_subgroup&oldid=15360