Linear groups saturated by subgroups of finite central dimension

TitleLinear groups saturated by subgroups of finite central dimension
Publication TypeJournal Article
Year of Publication2019
AuthorsSemko, NN, Skаskіv, LV, Yarovaya, OA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2019.06.003
Issue6
SectionMathematics
Pagination3-7
Date Published06/2019
LanguageEnglish
Abstract

Let F be a field, A be a vector space over F, and G be a subgroup of GL(F, A). We say that G has a dense family of subgroups having finite central dimension, if, for every pair of subgroups H, K of G such that H ≤ K and H is not maximal in K, there exists a subgroup L of finite central dimension such that H ≤ L ≤ K (we can note that L can match with one of the subgroups H or K). We study locally solvable linear groups with a dense family of subgroups having finite central dimension.

Keywordsdense family of subgroups, finite central dimension, infinite groups, infinite-dimensional linear group, linear group, locally soluble groups
References: 

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