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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 92–100
DOI: https://doi.org/10.4213/mzm8550
(Mi mzm8550)
 

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
Full-text PDF (446 kB) Citations (9)
References:
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
English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 88–95
DOI: https://doi.org/10.1134/S0001434610010116
Bibliographic databases:
UDC: 512.543
Language: Russian
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
Citation in format AMSBIB
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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