Maximal subgroups and chief factors of certain generalized soluble groups

Richard E. Phillips, Derek J. S. Robinson and James Edward Roseblade

Vol. 37 (1971), No. 2, 475–480

DOI: 10.2140/pjm.1971.37.475

Abstract

It is shown by means of a generalization of a result of R. Baer and D. H. McLain that if G is a locally polycyclic group and if the chief factors of every finitely generated subgroup of G have finite rank at most equal to r, then every maximal subgroup of G has index dividing the r th power of some prime. This answers a question about locally supersoluble groups raised by the first author. In addition, examples are furnished to show that neither of the properties “all chief factors are finite” and “all maximal subgroups have finite index” implies the other.

Mathematical Subject Classification 2000

Primary: 20E15

Milestones

Received: 21 September 1970

Published: 1 May 1971