Conjugacy separability of a class of 1-relator products

Abstract

We prove the conjugacy separability of groups of the form G = ⟨ a 1 , … a r , b 1 , … , b s : a i e i = b j f j = ( U ( a 1 , … , a r ) V ( b 1 , … , b s ) ) m = 1 ⟩ G = \langle {a_1}, \ldots {a_r},{b_1}, \ldots ,{b_s}:a_i^{{e_i}} = b_j^{{f_j}} = (U({a_1}, \ldots ,{a_r})V({b_1}, \ldots ,{b_s}) {)^m} = 1\rangle , where m > 1 m > 1 .