On decomposing one relator products of cyclic groups into free products with amalgamation

Abstract

This paper deals with the problem of decomposing some nitely generated groups into non-trivial free products with amalgamation. We consider this problem for so called one-relator products of cyclic groups. Let $G=<a,b | a^{2n}=R^m(a,b)=1>, where n=0 or n>1, m>1 and R(a,b) is a cyclically reduced word in the free group on a and b which involves b. Then G is a non-trivial free product with amalgamation.