Characteristic AEP-subgroup
From Groupprops
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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and AEP-subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition
A subgroup of a group
is termed a characteristic AEP-subgroup if the homomorphism:
that sends an automorphism of to its restriction to
is well-defined (i.e., every automorphism of
does restrict to an automorphism of
) and surjective (i.e., every automorphism of
arises as the restriction of an automorphism of
).