# FACPC-subgroup

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]

## Contents

## Definition

Suppose is a finite abelian group (i.e., a group that is both finite and abelian) and is a subgroup of . We say that is a **FACPC-subgroup** or **finite-abelian-characteristic-potentially characteristic** subgroup of if there exists a finite abelian group containing such that both and are characteristic subgroups of .

## Relation with other properties

### Stronger properties

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

Characteristic subgroup of finite abelian group |

### Weaker properties

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

Subgroup of finite abelian group | ||||

Characteristic-potentially characteristic subgroup |