Certain quotients of HNN-extensions which are HNN-extensions.
by
Arye Juhasz
Technion,Haifa, Israel

Let G be a group with an HNN-presentation P=<H, t - t^-1Ut=V >.Let R be a cyclically reduced word in G and let N be its normal closure in G.We give a sufficient condition on R in order that G/N has an HNN presentation Q, Q=<K, t - t^-1 Lt=M >, where H<K, U<L, V<M.We apply this to the case when G is a one-relator group and get a family of two relator groups with HNN-presentation.Under certain conditions this leads to a solution of the word problem and related problems.

Date received: February 9, 2006