Conjugation-invariantly relatively normal subgroup
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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
View other such properties
Definition
Suppose . We say that
is conjugation-invariantly relatively normal in
with respect to
if
is a normal subgroup in every conjugate of
in
that contains
.
Relation with other properties
Stronger properties
- Strongly closed subgroup
- Weakly closed subgroup: For proof of the implication, refer Weakly closed implies conjugation-invariantly relatively normal and for proof of its strictness (i.e. the reverse implication being false) refer Conjugation-invariantly relatively normal not implies weakly closed.