Conjugacy-closed Hall subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: conjugacy-closed subgroup and Hall subgroup
View other subgroup property conjunctions | view all subgroup properties


Symbol-free definition

A subgroup of a group is termed a conjugacy-closed Hall subgroup if it satisfies the following conditions:

  • It is conjugacy-closed: Any two elements of the subgroup that are conjugate in the whole group are conjugate in the subgroup.
  • It is a Hall subgroup: Its order and index are relatively prime.

Relation with other properties

Stronger properties

Weaker properties