# Center of pronormal subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

A subgroup $H$ of a group $G$ is termed a center of pronormal subgroup if there exists a pronormal subgroup $K$ of $G$ such that $H$ equals the center of $K$.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian pronormal subgroup |FULL LIST, MORE INFO
center of Sylow subgroup |FULL LIST, MORE INFO

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
characteristic central subgroup of pronormal subgroup characteristic central subgroup of pronormal subgroup (characteristic being in the pronormal subgroup)
central subgroup of pronormal subgroup
SCDIN-subgroup subset-conjugacy-determined subgroup in its normalizer center of pronormal implies SCDIN |FULL LIST, MORE INFO