Linear groups saturated by subgroups of finite central dimension

1Semko, NN
Skаskіv, LV
Yarovaya, OA
1State Tax Service National University of Ukraine, Irpin
Dopov. Nac. akad. nauk Ukr. 2019, 6:3-7
https://doi.org/10.15407/dopovidi2019.06.003
Section: Mathematics
Language: English
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.

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

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