Vol. 77, No. 1, 1978

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On prosupersolvable groups

B. C. Oltikar and Luis Ribes

Vol. 77 (1978), No. 1, 183–188
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
Authors
B. C. Oltikar
Luis Ribes