Potentially verbal 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

Definition with symbols

A subgroup H of a group G is termed a potentially verbal subgroup if there exists a group K containing G such that H is a verbal subgroup of K.

Formalisms

In terms of the potentially operator

This property is obtained by applying the potentially operator to the property: verbal subgroup
View other properties obtained by applying the potentially operator

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Potentially power subgroup |FULL LIST, MORE INFO
Finite-pi-potentially verbal 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 subgroup potentially verbal implies normal normal not implies potentially verbal Potentially fully invariant subgroup|FULL LIST, MORE INFO

Facts