Equally partitioned groups

I. Martin (Irving) Isaacs

Vol. 49 (1973), No. 1, 109–116

DOI: 10.2140/pjm.1973.49.109

Abstract

It is proved that the only finite groups which can be partitioned by subgroups of equal orders are the p-groups of exponent p. The connection between equally partitioned groups and Sperner spaces is discussed. It is also proved that finite groups partitioned by pairwise permutable subgroups are abelian.

Mathematical Subject Classification 2000

Primary: 20D99

Milestones

Received: 20 July 1972

Published: 1 November 1973