A finite $p$-group $P = AB$ with $\Core(A)=\Core(B)=\{1\}$

The Automorphism Group of a Finite p-Group is Almost Always a p-Group

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the thir...

Finite Groups with p-Sylow Coverings

Finite Group Actions on P ” ( C )

Consider the question: which finite groups operate as symmetries of the complex projective plane P’(C)? Any finite subgroup of &X,(C) acts as a group of collineations and these give the linear models. The list of such groups is relatively short [MBD] but contains, for example, a groups of rank < 2, subgroups of U(Z), and the simple groups A,, A,, an PSL(F,). It turns out that these linear group...

finite groups with p-sylow coverings

THE DERIVED SERIES OF A FINITE p-GROUP

Let G be a finite p-group, and let G denote the d-th term of the derived series of G . We show, for p > 5, that G 6= 1 implies logp |G | > 2 d + 3d − 6, and hence we improve a recent result by Mann.