Fully normalized and potentially fully invariant implies centralizer-annihilating endomorphism-invariant
From Groupprops
Statement
Suppose is a subgroup of a group
satisfying the following two conditions:
-
is a Fully normalized subgroup (?) of
, i.e., every automorphism of
extends to an inner automorphism of
.
-
is a Potentially fully invariant subgroup (?) of
, i.e., there exists a group
containing
in which
is a fully invariant subgroup.
Then, is a Centralizer-annihilating endomorphism-invariant subgroup (?) of
: For every endomorphism
of
whose kernel contains
,
.