Adjoining roots to conjugacy separable groups (Q1902128)

Some conditions so that, by adjoining roots to a group in certain classes of conjugacy separable groups, the resulting group is again conjugacy separable, are obtained. The result is applied to show that all residually finite 1-relator groups of the form \(\langle a,b\mid (a^{-\alpha} b^\beta a^\alpha b^\gamma) \rangle\) as well as groups of the form \(\langle a,b\mid (a^{-\alpha} b^\beta a^\alpha b^\gamma)^s \rangle\), where \(s>1\), are conjugacy separable.