Group whose center is normality-large
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 whose center is normality-large is a group such that the intersection of its center with any nontrivial normal subgroup is nontrivial.
Relation with other properties
Stronger properties
- Abelian group
- Nilpotent group
- Quasisimple group that is not simple (i.e., a perfect group with a nontrivial center, such that the quotient by the center is a simple group)