Pronormal 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: pronormal subgroup and Hall subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Definition with symbols

A subgroup H of a finite group G is termed a pronormal Hall subgroup if it satisfies the following two conditions:

  1. H is a Hall subgroup of G: The order and index of H in G are relatively prime.
  2. H is a pronormal subgroup of G: If K is a conjugate subgroup to H in G, then H, K are conjugate subgroups inside \langle H, K \rangle.

Relation with other properties

Stronger properties

Weaker properties