Rasoul Soleimani - Department of Mathematics, Payame Noor University (PNU), Iran

Let G be a finite group, AutZ(G) denote the group of all automorphisms of G centralizing G/Z, andAutZ(G) the group of all automorphisms of G centralizing Z elementwise, where Z = Z(G). Moreover,AutZZ(G)=(…)Let cza(G) be the number of the orbits generated by the action on G of the group of AutZZ(G). In this paper, we classifies all the finite groups G with cza(G) ≥ ۷