Cohomology Theory of Groups with a Single Defining Relation

The Word Problem is that of determining when two elements of F (or two 'words') represent the same element of G, or, equivalently, when a given element W of F lies in R, and so can be written in the form (1). Magnus has solved this problem for the case n = 1, of a single defining relation.3 A complementary problem is that of uniqueness for expressions of the form (1), or more simply that of determining all identities among the relations R,, * **, Rn Xof the form