Bondarenko V. Applications of matrix problems in group theory and algebraic geometry

One investigates properties of the unitriangular and triangular representations of nite groups over elds. It is completely described (in both cases) the modular representations of the cyclic group of order 2, and unitriangular and triangular wild groups. One investigates the conjugacy classes of the groups of unitriangular matrices over a eld of characteristic 2 in the case when they consist of elements of order 2. For such classes one indicates a full list of (canonical) representatives. The number of such classes over a nite elds are calculated. It is proved, that if a hypersurface singularity of dimension n >= 2 is given by equations without terms of degree d <= 3, then it is Cauhen-Macaulay wild. It is also proved, that if a hypersurface singularity of dimension n >= 3 is given by equations without terms of degree d <= 2, then it is also Cauhen-Macaulay wild.