Conjugacy-closed Hall subgroup
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
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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.