On roots and subsemigroups of nilpotent groups

Abstract:

${E_\omega },{U_\omega }$ and ${D_\omega }$ semigroups are defined by extrapolating the definitions of their group counterparts; and a class $n$ semigroup is defined to be a subsemigroup of a class $n$ group. The purpose of this paper is to show that a class $n{E_\omega }$ semigroup generates an ${E_\omega }$ group and that a class $n$ semigroup is ${U_\omega }$ if and only if it generates a ${U_\omega }$ group.