# Center of pronormal subgroup

From Groupprops

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]

## Contents

## Definition

A subgroup of a group is termed a **center of pronormal subgroup** if there exists a pronormal subgroup of such that equals the center of .

## 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 |