Sylow subgroup of permutable subgroup

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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: Sylow subgroup and permutable subgroup
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Definition

A subgroup of a finite group is termed a Sylow subgroup of permutable subgroup if it satisfies the following equivalent conditions:

  • It can be expressed as a Sylow subgroup of a permutable subgroup of the whole group.
  • It can be expressed as the intersection of a Sylow subgroup of the whole group and a permutable subgroup of the whole group.

Relation with other properties

Stronger properties