Let α be a coprime automorphism of group G prime order and let P an α-invariant Sylow p-subgroup G. Assume that p∉π(CG(α)). Firstly, we prove is p-nilpotent if only CNG(P)(α) centralizes P. In the case Sz(2r) PSL(2,2r)-free where r=|α|, show p-closed CG(α) normalizes As consequence these two results, obtain G≅P×H for H We also generalization Frobenius p-nilpotency theorem groups admitting autom...

It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group.

In this paper we study a key exchange protocol similar to the DiffieHellman key exchange protocol, using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no. 92 of the Hall-Senior table [16] to an arbitrary prime p and show that, for those groups, the group of central automorphisms is commutative. We use these for the key exchange we are stu...