Powerful p-groups have non-inner automorphisms of order p and some cohomology

COHOMOLOGY OF UNIFORMLY POWERFUL p-GROUPS

In this paper we will study the cohomology of a family of p-groups associated to Fp-Lie algebras. More precisely we study a category BGrp of p-groups which will be equivalent to the category of Fp-bracket algebras (Lie algebras minus the Jacobi identity). We then show that for a group G in this category, its Fp-cohomology is that of an elementary abelian p-group if and only if it is associated ...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

ON AUTOMORPHISMS OF SOME FINITE p-GROUPS

We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Autc(G) = Inn(G), where Autc(G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Autc(G) ∼= Autc(H). Finally we study class preserving automorphisms of groups o...

Finite P-groups of Class 2 Have Noninner Automorphisms of Order P

We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.

some inequalities for nilpotent multipliers of powerful p-groups