# Group in which every characteristic subgroup is powering-invariant

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

A **group in which every characteristic subgroup is powering-invariant** is a group in which every characteristic subgroup is a powering-invariant subgroup.

## Relation with other properties

### Stronger properties

### Incomparable properties

### Conjecture

The conjecture that every characteristic subgroup of nilpotent group is powering-invariant is currently open. The conjecture states that the property of being a nilpotent group is stronger than the property of being a group in which every characteristic subgroup is powering-invariant.