Coprime automorphism-faithful characteristic subgroup

From Groupprops
Revision as of 21:34, 6 July 2008 by Vipul (talk | contribs) (New page: {{wikilocal}} {{subgroup property conjunction|characteristic subgroup|coprime automorphism-faithful subgroup}} ==Definition== A subgroup <math>H</math> of a finite group <math>G<...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and coprime automorphism-faithful subgroup
View other subgroup property conjunctions | view all subgroup properties


A subgroup H of a finite group G is termed copime automorphism-faithful characteristic if every automorphism of G restricts to an automorphism of H (i.e., H is a characteristic subgroup) and if K is the kernel of the map:

\operatorname{Aut}(G) \to \operatorname{Aut}(H)

defined by restriction, then every prime divisor of the order of K, divides the order of G.