Bondarenko V. Classifition problems in the theory of modular representations of groups

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0501U000025

Applicant for

Specialization

  • 01.01.06 - Алгебра і теорія чисел

15-01-2001

Specialized Academic Board

Д 26.001.18

Taras Shevchenko National University of Kyiv

Essay

All finite groups, the problem of classifying the representations of which is tame, is described. The full classification of modular representation of quasidiedral groups is obtained. The description of all indecomposable representation of arbitrary bundle of semichains is obtained. The solution of the well-known Gelfand's problem and its generalization is obtained (in explicit form). All faithful partially ordered set of finite growth is described. The problem about one operator on a vector space, gradable by a partially ordered set with involution, is obtained. For any minimal polynomial, all tame and wild cases are described.

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