Tylyshchak O. Matrix representations of finite groups over commutative local rings and their applications

The thesis is devoted to the studding of matrix representations of finite groups over commutative rings, the studding of monomial matri¬ces connected with representations over the same rings and to the diversified applications of methods of theory of matrix representati¬ons of finite groups over commutative rings in linear group theory, group rings, and coding theory. The paper deals mainly with irreduci¬ble and indecomposable modular representations of finite p-groups over commutative rings of characteristic ps, which are not fields. In paper it has been found the criterion of finiteness of the set of non-equivalent irreducible matrices representations of given degree of finite p-group over a commutative Noetherian local ring of characteristics ps (s > 0, p is a prime) which is not semi-primitive ring, with infinite residue class field. It has also been shown the infiniteness of the set of non-equivalent irreducible matrix representations of given degree n > 1 of finite p-group G of order |G| > 2 over a commutative Noetherian local semi-primordial non-integer ring of characteristic p, with infinite residue class field.