On conjugacy p-separability of free centre-by-metabelian groups

Abstract

AbstractA group G is said to be conjugacy p-separable if two non-conjugate elements of G remain non-conjugate in some finite p-group endomorphic image of G. We show that the non-cyclic free centre-by-metabelian groups are not conjugacy p-separable for any prime p. On the other hand, we show that every free centre-by-metabelian group has the solvable conjugacy problem