We characterize the rational subsets of a finite group and discuss the relations to integral Cayley graphs‎.

‎We characterize those groups $G$ and vector spaces $V$ such that $V$ is a faithful irreducible $G$-module and such that each $v$ in $V$ is centralized by a $G$-conjugate of a fixed non-identity element of the Fitting ...

Let $gamma(S_n)$ be the minimum number of proper subgroups‎ ‎$H_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $S_n$ such that each element in $S_n$‎ ‎lies in some conjugate of one of the $H_i.$ In this paper we‎ ‎conjecture ...

We exhibit an explicit construction for the second cohomology group $H^2(L, A)$ for a Lie ring $L$ and a trivial $L$-module $A$. We show how the elements of $H^2(L, A)$ correspond one-to-one to the equivalence classes of ...