An Application of Word Combinatorics to Decision Problems in Group Theory

Juhász, Arye

doi:10.1007/978-3-7643-9911-5_7

Arye Juhász⁵

Part of the book series: Trends in Mathematics ((TM))

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Abstract

In this work we develop a graph theoretical test on graphs corresponding to subgroups of one-relator groups with small cancellation condition which, if successful, implies that the subgroup under consideration has solvable membership problem with a simple solution. The proof of the solvability of the membership problem relies on word combinatorics in an essential way.

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References

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Authors and Affiliations

Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel
Arye Juhász

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Arye Juhász
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Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany
Oleg Bogopolski
School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada
Inna Bumagin
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St., West, Montreal, Quebec, H3A 2K6, Canada
Olga Kharlampovich
Departament de Matematica Aplicada III, EPSEM — Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73, 08242, Manresa, Barcelona, Spain
Enric Ventura

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Juhász, A. (2010). An Application of Word Combinatorics to Decision Problems in Group Theory. In: Bogopolski, O., Bumagin, I., Kharlampovich, O., Ventura, E. (eds) Combinatorial and Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9911-5_7

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DOI: https://doi.org/10.1007/978-3-7643-9911-5_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9910-8
Online ISBN: 978-3-7643-9911-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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