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The word problem for small cancellation quotients of groups acting on trees

Published online by Cambridge University Press:  14 November 2011

R. M. S. Mahmud
R. M. S. Mahmud
Affiliation:
Department of Mathematics, University of Bahrain, P.O. Box 32038, Isa Town, State of Bahrain
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Synopsis

The small cancellation theory over free products with amalgamation and HNN groups is extended to groups acting on trees in which the action with inversions is possible. This will include the case of tree products of groups and treed-HNN groups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 3-4 , 1992 , pp. 361 - 374
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

1Dicks, W.. Groups, Trees and Projective Modules, Lecture Notes in Mathematics 790 (Berlin: Springer, 1980).CrossRefGoogle Scholar
2Lyndon, R. C.. On Dehn's algorithm. Math. Ann. 166 (1966), 208–28.CrossRefGoogle Scholar
3Lyndon, R. C. and Schupp, P. E.. Combinatorial group theory (Berlin: Springer, 1977).Google Scholar
4Mahmud, R. M. S.. On groups acting on trees (Ph.D. Thesis, University of Birmingham, U.K., 1984).Google Scholar
5Mahmud, R. M. S.. Presentation of groups acting on trees with inversions. Proc. Roy. Soc. Edinburgh Sect. A 113 (1989), 235–241.CrossRefGoogle Scholar
6Mahmud, R. M. S.. The normal form theorem of groups acting on trees with inversions. J. Univ. Kuwait (Sci) 17 (1990).Google Scholar
7Mahmud, R. M. S.. The conjugacy theorem of groups acting on trees with inversions (in preparation).Google Scholar
8Miller, C. F. III.On group-theoretic decision problems and their classification, Ann. of Math. Studies 68 (Princeton: Princeton University Press, 1971).Google Scholar
9Perraud, J.. Sur la condition de petite simplification C'(1/6) dans un produit libre amalgam. C.R. Acad. Sci. Paris Sir. I Math. 291 (1980), 247–250.Google Scholar
10Perraud, J.. Conditions de petites simplifications dans un HNN extension. Groups-St Andrews 1981conference, London Mathematical Society Lecture Note Series 71 (Edinburgh: Cambridge University Press, 1981).Google Scholar
11Rabin, M. O.. Recursive unsolvability of group theoretic problems. Ann. of Math. 67 (1958), 172–174.CrossRefGoogle Scholar
12Schupp, P. E.. Small cancellation theory over free products with amalgamation. Math. Ann. 193 (1971), 255–64.CrossRefGoogle Scholar
13Schupp, P. E.. A survey of small cancellation theory. In Word Problem I, pp. 269–89 (Amsterdam: North-Holland, 1973).Google Scholar