REIDEMEISTER CLASSES IN WREATH PRODUCTS OF ABELIAN GROUPS

Among restricted wreath products G (sic)Z(k) , where G is a finite abelian group, we find three large classes of groups admitting an automorphism phi with finite Reidemeister number R( phi) (number of phi-twisted conjugacy classes). In other words, groups from these classes do not have the R-infinity property. Moreover, we prove that if phi is a finite order automorphism of G(sic)Z(k) with R(phi) < infinity; then R(phi) is equal to the number of fixed points of the map [rho] -> [rho o phi] defined on the set of equivalence classes of finite dimensional irreducible unitary representations of G(sic) Z(k).