No abstract

We know that if Γ is the automorphisem group of primitive tournament T = (X, U), then Γ = H • G where H = (X, +), G is irreducible solvable subgroup in GL n, p k with an odd order. But there are three kinds of irreducible solvable subgroups in GL n, p k : imprimitive groups, affine primitive groups, and nonaffine primitive groups. In this paper we will study the structure of nonaffine primitive solvable subgroups in GL 3, p k , find the order of these subgroups, and show that all nonaffine primitive solvable subgroups in GL 3, p k have an even order, and then there are no primitive tournaments as automorphisem group Γ = H • G where G is nonaffine primitive solvable subgroups in GL 3, p k .

In this paper, we determine when two Cayley graphs over the cyclic group Z pq 2 are to be isomorphic, for p = q prime numbers. and we determine the all types of automorphism groups of these graphs.