On prosupersolvable groups

B. C. Oltikar and Luis Ribes

Vol. 77 (1978), No. 1, 183–188

DOI: 10.2140/pjm.1978.77.183

Abstract

Let G be a prosupersolvable group (projective limit of finite supersolvable groups), whose order involves only finitely many primes; then we show that G is topologically finitely generated iff its Frattini subgroup is open in G. If a prosupersolvable group G is topologically finitely generated, so is each Sylow p-subgroup of G. If G is a topologically finitely generated prosupersolvable group, then every subgroup G of finite index is open.

Mathematical Subject Classification 2000

Primary: 20E18

Milestones

Received: 6 May 1977

Revised: 8 December 1977

Published: 1 July 1978