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.

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