A simple construction of semigroups all of whose subsemigroups are left ideals.
A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.
Let be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly prime divisors. We show that such groups are solvable whenever . Moreover, we prove that if is a non-solvable group with this property, then and is an extension of or by a solvable group.