Namespaces
Variants
Actions

Characteristic subgroup

From Encyclopedia of Mathematics
Jump to: navigation, search

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


Comments

Examples of characteristic subgroups are the centre of a group, denoted by $Z(G)$, the Fitting subgroup, $F(G)$, the commutator subgroup, $D(G)$, $[G,G]$ or $G'$, the Frattini subgroup, $\Phi(G)$, the socle, $\mathrm{Socl}(G)$, the layer, $E(G)$, 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://www.encyclopediaofmath.org/index.php?title=Characteristic_subgroup&oldid=35104
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article