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.
Mathematics Subject Classification (2000)
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Juhász, A. Small cancellation theory with unified small cancellation condition. J. London. Math. Soc. 2 (40):57–80 (1989).
Juhász, A. Solution of the membership problem of Magnus subgroups of onerelator free products with small cancellation condition. In: Algebra and Geometry in Geneva and Barcelona, “Asymptotic and Probabilistic Methods in Geometric Group Theory”, Geneva, June 2005 and “Barcelona Group Theory Conference”, Barcelona, July 2005, 169–195, Birkhäuser (2007).
Juhász, A. A Freiheitssatz for Whitehead graphs of one-relator groups with small cancellation. Communications in Algebra 37:8, 2714–2741 (2009).
Johnson, D.L. Topics in the Theory of Group Presentations. LMSLNS, Cambridge University Press, Cambridge. 42 (1980).
Lyndon, R.C., Schupp, P.E. Combinatorial Group Theory, Springer-Verlag, Berlin-Heidelberg-New York, (1977).
Magnus, W., Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann. 106 pp. 295–307 (1932).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Basel AG
About this paper
Cite this paper
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
Download citation
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)