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This article is cited in 9 scientific papers (total 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.
Received: 05.02.2009 Revised: 27.04.2009
Citation:
D. I. Moldavanskii, “The Intersection of the Subgroups of Finite Index in Baumslag–Solitar Groups”, Mat. Zametki, 87:1 (2010), 92–100; Math. Notes, 87:1 (2010), 88–95
Linking options:
https://www.mathnet.ru/eng/mzm8550https://doi.org/10.4213/mzm8550 https://www.mathnet.ru/eng/mzm/v87/i1/p92
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