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 on the group ring of a finite group, bearing in mind further applications to topology.