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Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2015-2015

FUNDING AMOUNT

N/A

ABSTRACT

The project is aimed at the development of the calculus of involutions and the local analysis of infinite groups with finite elements with applications in the theories of almost-regions, (multiply) transitive groups, groups with 3-transpositions, groups with finite, perfect involutions and given subgroups, finitely approximable and factorizable groups. It is planned to further develop the theory of infinite doubly transitive permutation groups, groups with finite, perfect, almost perfect involutions, and additional conditions for 3-transitivity, strong nesting and isolation of given subgroups. A generalization of the classical theorems of Frobenius, Burnside, Zassenhaus, Brauer-Suzuki, Higman, Suzuki, Bender, Shunkov, Kegel, and others to classes of periodic and mixed groups with finite involutions. Investigation of almost-regions and exactly doubly transitive groups, elucidation of their more detailed structure, generalization of some well-known theorems of Jordan, Zassenhaus, M. Hall, Grötzer, Karzel, Kirby, Wefelscheid, Veling, Mazurov, etc. A study of the group of bounded permutations of the set of natural Numbers $ N $ and permutation groups of the set $ N $ with finite scattering parameters. Construction of new examples of periodic finitely approximable groups and elucidation of the structure of certain Famine groups. Find co-representations of groups with 3-transpositions close to the presentation of finite Coxeter groups. Computer modeling of groups. More... »

URL

http://www.rfbr.ru/rffi/ru/project_search/o_2000308

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