Fully normalized potentially fully invariant subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: fully normalized subgroup and potentially fully invariant subgroup
View other subgroup property conjunctions | view all subgroup properties
- is a fully normalized subgroup of , i.e., every automorphism of arises as the restriction to of an inner automorphism of .
- is a potentially fully invariant subgroup of , i.e., there exists a group containing such that is a fully invariant subgroup of .
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|centralizer-annihilating endomorphism-invariant subgroup||fully normalized and potentially fully invariant implies centralizer-annihilating endomorphism-invariant|
|normal fully normalized subgroup||follows from potentially fully invariant implies normal|