Abstract
In this paper we develop a generalization of the small cancellation theory. The usual small cancellation hypotheses are replaced by some condition that, roughly speaking, says that if a common part of two relations is a big piece of one relation then it must be a very small piece of another. In particular, we show that a finitely presented generalized small cancellation group has a solvable word problem. The machinery developed in the paper is to be used in the following papers of this series for constructing some group-theoretic examples.
Similar content being viewed by others
References
R. C. Lyndon and P. E. Schupp,Combinatorial Group Theory, Springer, Berlin-Heidelberg-New York, 1977.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rips, E. Generalized small cancellation theory and applications I. The word problem. Israel J. Math. 41, 1–146 (1982). https://doi.org/10.1007/BF02760660
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02760660