Sylow-relatively strongly closed subgroup

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Definition

Suppose $P$ is a group of prime power order and $H$ is a subgroup of $P$ . We say that $H$ is a Sylow-relatively strongly closed subgroup if, for any finite group $G$ containing $P$ as a Sylow subgroup, $H$ is a strongly closed subgroup of $P$ with respect to $G$ .

Relation with other properties

Stronger properties

Subisomorph-containing subgroup of group of prime power order

Weaker properties