Group whose center is normality-large

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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)

Weaker properties

• Group in which every nontrivial normal subgroup contains a cyclic normal subgroup

Opposite properties

• Centerless group