Almost quasisimple group

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