A simple proof of Vinogradov’s theorem on the orderability of the free product of -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.
The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigroup is a rpp-semigroup with left central idempotents if and only if it is a right bin.