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Residually finite tubular groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  27 August 2019

Nima Hoda ,
Daniel T. Wise  and
Daniel J. Woodhouse
Nima Hoda
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski pl., Grunwaldzki 2/4, 50–384 Wrocław, Poland (nima.hoda@mail.mcgill.ca)
Daniel T. Wise
Affiliation:
Department of Mathematics & Statistics, McGill University Montreal, QC, Canada H3A0B9 (wise@math.mcgill.ca)
Daniel J. Woodhouse
Affiliation:
Department of Mathematics, Technion Haifa 32000, Israel (woodhouse.da@campus.technion.ac.il)
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Abstract

A tubular group G is a finite graph of groups with ℤ2 vertex groups and ℤ edge groups. We characterize residually finite tubular groups: G is residually finite if and only if its edge groups are separable. Methods are provided to determine if G is residually finite. When G has a single vertex group an algorithm is given to determine residual finiteness.

Keywords

Residually FiniteTubular Groups

MSC classification

Primary: 20E26: Residual properties and generalizations; residually finite groups

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 2937 - 2951
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

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