Subgroups of finite index in profinite groups

Michael Peter Anderson

Vol. 62 (1976), No. 1, 19–28

DOI: 10.2140/pjm.1976.62.19

Abstract

A profinite group is called strongly complete if every subgroup of finite index is open and of type (AF) if it has only finitely many subgroups of any fixed index. In this paper it is shown that a topologically finitely generated abelian by pro-nilpotent profinite group is strongly complete, and that a pro-solvable profinite group is strongly complete if is of type (AF).

Mathematical Subject Classification

Primary: 20E20, 20E20

Milestones

Received: 25 February 1975

Revised: 19 June 1975

Published: 1 January 1976