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=35103
Characteristic subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_subgroup&oldid=35103
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article