Algebra Discrete Math., 2020 Volume 29, Issue 1, Pages 1–32
(Mi adm735)
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 Abstract:
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.
Keywords:
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 Received: 20.12.2019
Language: English
DOI:
10.12958/adm1516
© , 2024
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