On invariant tensors on the group ring of finite groups

In several papers author applied methods of algebraic topology to some topics in general topology; main applications are in dimension theory. An important tool of these investigations were two new types of spectral sequences. The first among them coincides with Cartan-Grothendieck sequence and thus involves the cohomology of a finite group. A description of second spectral sequence needs a new type of homology (cohomology) of a finite group which based on skew-symmetric invariant functions on the group ring of a finite group. The purpose of this article is to give a few principal approaches to study the structure of skew-symmetric invariant functions and, generally, of skew-symmetrical invariant tensors oil the group ring of a finite group, bearing in mind further applications to topology. (C) 2008 Published by Elsevier B.V.