Vol. 36, No. 2, 1971

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Intersections of nilpotent Hall subgroups

Marcel Herzog

Vol. 36 (1971), No. 2, 331–333
Abstract

A family of subgroups of a finite group G is said to satisfy (property) B if whenever U = H1 Hr is a representation of U as intersection of elements of 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 Sπ(G) then H1 H2 ⊲ H1. Then Sπ(G) satisfles B.

Mathematical Subject Classification
Primary: 20.43
Milestones
Received: 3 June 1970
Published: 1 February 1971
Authors
Marcel Herzog