Geodesic
Linear groups saturated by subgroups of finite central dimension
Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 117-128

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $F$ be a field, $A$ be a vector space over $F$ and $G$ be a subgroup of $\mathrm{GL}(F,A)$. 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 $H\leqslant K$ and $H$ is not maximal in $K$ there exists a subgroup $L$ of finite central dimension such that $H\leqslant L\leqslant K$. In this paper we study some locally soluble linear groups with a dense family of subgroups, having finite central dimension.
Keywords: linear group, infinite group, infinite dimensional linear group, dense family of subgroups, locally soluble group, finite central dimension. 
@article{ADM_2020_29_1_a10,
     author = {N. N. Semko and L. V. Skaskiv and O. A. Yarovaya},
     title = {Linear groups saturated by subgroups of finite central dimension},
     journal = {Algebra and discrete mathematics},
     pages = {117--128},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a10/}
}
TY  - JOUR
AU  - N. N. Semko
AU  - L. V. Skaskiv
AU  - O. A. Yarovaya
TI  - Linear groups saturated by subgroups of finite central dimension
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 117
EP  - 128
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a10/
LA  - en
ID  - ADM_2020_29_1_a10
ER  - 
%0 Journal Article
%A N. N. Semko
%A L. V. Skaskiv
%A O. A. Yarovaya
%T Linear groups saturated by subgroups of finite central dimension
%J Algebra and discrete mathematics
%D 2020
%P 117-128
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a10/
%G en
%F ADM_2020_29_1_a10
N. N. Semko; L. V. Skaskiv; O. A. Yarovaya. Linear groups saturated by subgroups of finite central dimension. Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 117-128. http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a10/