Small cancellation theory

Summary

Small cancellation theory studies groups given by presentations whose relators have only short common pieces. Under such conditions, such as $C'(1/6)$, a nontrivial word equal to the identity must contain a long part of some relator. This gives Dehn's algorithm for the word problem, and finitely presented $C'(1/6)$ groups are hyperbolic. The theory is also a tool to build groups with unusual properties, as in the construction of Tarski monster groups.