Isomorph-normal coprime automorphism-invariant subgroup
From Groupprops
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: isomorph-normal subgroup and coprime automorphism-invariant subgroup
View other subgroup property conjunctions | view all subgroup properties
Contents
Definition
A subgroup of a finite group
is termed isomorph-normal coprime automorphism-invariant if it satisfies the following two conditions:
-
is isomorph-normal in
: Every subgroup of
isomorphic to
is a normal subgroup of
.
-
is a coprime automorphism-invariant subgroup of
: Any automorphism
of
whose order is relatively prime to the order of
satisfies
.