This article is cited in 18 papers

Everywhere Dense Subgroups of One Group of Tree Automorphisms

E. L. Pervova

Chelyabinsk State University

Abstract: The well-known question of the existence, in the Grigorchuk 2-groups, of subgroups that are everywhere dense in the profinite topology is answered negatively. This is shown to be equivalent to the fact that these groups do not contain maximal subgroups of infinite index.

UDC: 512.54

Received in February 2000

 English version: Proceedings of the Steklov Institute of Mathematics, 2000, 231, 339–350

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