Order-conjugate Hall subgroup

Definition
A subgroup of a group is termed an order-conjugate Hall subgroup if it satisfies the following two conditions:


 * It is a defining ingredient::Hall subgroup: its order and index are relatively prime.
 * It is an defining ingredient::order-conjugate subgroup: it is conjugate to any subgroup of the same order.

Stronger properties

 * Weaker than::Sylow subgroup
 * Weaker than::Normal Hall subgroup
 * Weaker than::Order-dominating Hall subgroup: