This article is cited in 9 papers

The Intersection of the Subgroups of Finite Index in Baumslag–Solitar Groups

D. I. Moldavanskii

Ivanovo State University

Abstract: For any one-relator group in the family of Baumslag–Solitar groups, a system of its elements is indicated whose normal closure in the group coincides with the intersection of all normal finite-index subgroups. The well-known criterion for the residual finiteness of Baumslag–Solitar groups is an immediate consequence of this result. It is also shown that, if the intersection of all finite-index normal subgroups in a Baumslag–Solitar group differs from the identity subgroup (i.e., if the group is not residually finite), then this intersection cannot be the normal closure of any finite set of elements.

Keywords: Baumslag–Solitar group, finite-index subgroup, one-relator group, residual finiteness, normal closure, amalgamated product.

UDC: 512.543

Received: 05.02.2009
Revised: 27.04.2009

DOI: 10.4213/mzm8550

 English version: Mathematical Notes, 2010, 87:1, 88–95

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