M. R. Dixon, L. A. Kurdachenko, N. N. Semko, I. Ya. Subbotin, “On some topics in the theory of infinite dimensional linear groups”, Algebra Discrete Math., 2020, том 29, выпуск 1,страницы 1

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SURVEY ARTICLE

On some topics in the theory of infinite dimensional linear groups

M. R. Dixon^a, L. A. Kurdachenko^b, N. N. Semko^c, I. Ya. Subbotin^d

^a Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.
^b Department of Algebra, Faculty of Mathematics and Mechanics, National University of Dnepropetrovsk, Gagarin prospect 72, Dnipro 10, 49010, Ukraine
^c Department of Mathematics, National State Tax Service Academy of Ukraine, 09200 Irpin, Ukraine
^d Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, U.S.A

Аннотация: In this paper we present a synopsis of some recent results concerned with infinite dimensional liner groups, including generalizations of irreducibility, the central dimension of a linear group, groups with finite dimensional orbits and the maximal and minimal conditions on subgroups of infinite central dimension.

Ключевые слова: finite central dimension, irreducible group, quasi-irreducible group, FC-hypercentral, augmentation dimension, finite orbit, finite dimensional orbit, minimal condition, maximal condition.

MSC: Primary 20H25; Secondary 20F29, 20E34

Поступила в редакцию: 20.12.2019

Язык публикации: английский

DOI: 10.12958/adm1516