# Almost quasisimple group

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

## Definition

A group is termed an **almost quasisimple group** if it has a self-centralizing normal subgroup that is a quasisimple group.

Note that for such a group, the self-centralizing quasisimple normal subgroup is unique (and hence also a characteristic subgroup) and is also the only component of the group, hence also equals the commuting product and the generalized Fitting subgroup of the group.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

simple non-abelian group | ||||

almost simple group | ||||

quasisimple group |