# Abelian-potentially verbal subgroup

From Groupprops

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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 of an abelian group is an **abelian-potentially verbal subgroup** if there exists an abelian group containing such that is a verbal subgroup of .

## Relation with other properties

### Stronger properties

property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|

Verbal subgroup of abelian group | |FULL LIST, MORE INFO | |||

Subgroup of finite abelian group | |FULL LIST, MORE INFO |

### Weaker properties

property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|

Abelian-potentially fully invariant subgroup | fully invariant not implies abelian-potentially verbal | |||

Abelian-potentially characteristic subgroup | ||||

Subgroup of abelian group |