Adjoining Roots to Conjugacy Separable Groups Original Research Article

In general, groups obtained by adjoining roots to conjugacy separable groups need not be conjugacy separable. We derive some conditions so that, by adjoining roots to certain classes of conjugacy separable groups, the resulting groups are again conjugacy separable. We apply this result to show that all residually finite 1-relator groups of the form left angle bracketa, b; a−αbβaαbγright-pointing angle bracket are conjugacy separable. We also show that groups of the form left angle bracketa, b; (a−αblaαbm)sright-pointing angle bracket, where s > 1, are conjugacy separable.