On the finite images of some one-relator groups

Abstract

It is shown that the group G = ⟨ a , b ; a − 1 b a = b k ⟩ ( k ≠ 0 ) G = \langle a,b;{a^{ - 1}}ba = {b^k}\rangle (k \ne 0) is determined in the class of all residually finite one-relator groups by the set of its finite images.