Whitehead torsion and group actions

A Non-reflexive Whitehead Group

We prove that it is consistent that there is a non-reflexive Whitehead group, in fact one whose dual group is free. We also prove that it is consistent that there is a group A such that Ext(A,Z) is torsion and Hom(A,Z) = 0. As an application we show the consistency of the existence of new co-Moore spaces.

The Whitehead Categorical Group of Derivations

Given a categorical crossed module H→ G, where G is a group, we show that the category of derivations, Der(G,H), from G into H has a natural monoidal structure. We introduce the Whitehead categorical group of derivations as the Picard category of Der(G,H) and then we characterize the invertible derivations, with respect to the tensor product, in this monoidal category. 2000 Mathematics Subject ...

The First Almost Free Whitehead Group Sh914

Assume G.C.H. and κ is the first uncountable cardinal such that there is a non-free κ-free abelian Whitehead group of cardinality κ. We prove that if all κ-free Abelian group of cardinality κ are Whitehead then κ is necessarily an inaccessible cardinal.

Convers - actions around integrated curriculum Presented by Kay Whitehead

Group Actions and Group Extensions

In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p)r acts freely on (S1)k , then r ≤ k.