Intersections of nilpotent Hall subgroups

Marcel Herzog

Vol. 36 (1971), No. 2, 331–333

DOI: 10.2140/pjm.1971.36.331

Abstract

A family ℋ of subgroups of a finite group G is said to satisfy (property) B^∗ if whenever U = H₁ ∩⋯ ∩ H_r is a representation of U as intersection of elements of ℋ of minimal length r, then r ≦ 2. The aim of this paper is to prove THEOREM 1. Let H be a nilpotent Hall π-subgroup of a group G and assume that if H₁,H₂ ∈ S_π(G) then H₁ ∩ H₂ ⊲ H₁. Then S_π(G) satisfles B^∗.

Mathematical Subject Classification

Primary: 20.43

Milestones

Received: 3 June 1970

Published: 1 February 1971