Characteristic subgroup
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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