# NSCFN-realizable group

From Groupprops

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

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

## Definition

A group is termed **NSCFN-realizable** if it satisfies the following equivalent conditions:

- can be embedded as a NSCFN-subgroup of some group.
- Given any homomorphism , there exists a group containing as a normal subgroup with isomorphic to , and the induced outer action of on is .
- The outer action cohomology class in is trivial.

## Relation with other properties

### Stronger properties

- Group whose center is a direct factor
- Abelian group
- Centerless group
- Group in which every automorphism is inner