Local powering-invariant normal subgroup
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 |