Stoika M. Matrix representations groups and crossed group rings over local commutative rings.

The thesis is devoted to the study of matrix representations of groups and crossed group rings over commutative rings. One receives a relationship between wildness of the problem of the description of matrices over integral domain up to equivalence modulo maximal ideal and properties of the set of simple elements of the given domain. One founds sufficient conditions of wildness of a finite 2 -groups over an arbitrary local factorial ring of characteristic zero with residue field of characteristic 2 . One proves wildness of the crossed group ring of abelian groups of type (4,4), (2,2,2) and the the ring of 2 -adic numbers with arbitrary non-degenerate system of factors. One describes the wild crossed group rings of a cyclic 2 -group and the ring of 2 -adic numbers with any system factors and an abelian 2-group and the ring of 2 -adic numbers with unit system of factors. One receives the criterion of tameness of finite p-groups over the ring of p -adic numbers with respect to projective representations.