Normal-potentially fully invariant subgroup

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of a group G is termed a normal-potentially fully invariant subgroup of G if there exists a group K containing G as a normal subgroup, such that H is a fully invariant subgroup of K.

Formalisms

In terms of the normal-potentially operator

This property is obtained by applying the normal-potentially operator to the property: fully invariant subgroup
View other properties obtained by applying the normal-potentially operator

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Fully invariant subgroup |FULL LIST, MORE INFO
Central subgroup of finite group Normal-potentially verbal subgroup|FULL LIST, MORE INFO
Normal-potentially verbal subgroup |FULL LIST, MORE INFO
Fully invariant-potentially fully invariant subgroup |FULL LIST, MORE INFO

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Potentially fully invariant subgroup |FULL LIST, MORE INFO
Normal-potentially characteristic subgroup |FULL LIST, MORE INFO
Normal subgroup Potentially fully invariant subgroup|FULL LIST, MORE INFO