Local powering-invariant normal subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: local powering-invariant subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Statement

A subgroup of a group is termed a local powering-invariant normal subgroup if it is both a local powering-invariant subgroup and a normal subgroup of the whole group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
quotient-local powering-invariant subgroup follows from quotient-local powering-invariant implies local powering-invariant local powering-invariant and normal not implies quotient-local powering-invariant |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
local powering-invariant subgroup |FULL LIST, MORE INFO
powering-invariant normal subgroup |FULL LIST, MORE INFO
powering-invariant subgroup |FULL LIST, MORE INFO