Small cancellation theory with a weakened small cancellation hypothesis. I. The basic theory

Abstract

We introduce a new small cancellation condition, the condition W(4), which weakens the condition C(4) & T(4), and develop the corresponding small cancellation theory. In this paper we develop the basic theory and prove a version of Greendlinger’s Lemma. In the forthcoming papers with the same title we prove the word problem and the conjugacy problem for groups having a presentation which satisfies the condition W(4).