Linear groups with minimality condition for some infinite-dimensional subgroups

• Date: 2005
• Main Authors: Dixon, M. R., Evans, M. J., Kurdachenko, L. A., Диксон, М. Р., Эванс, М., Курдаченко, Л. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3702
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $F$ be a field, let $A$ be a vector space over $F$, and let $GL(F, A)$ be the group of all automorphisms of the space $A$. If $H$ is a subgroup of $GL(F, A)$, then we set aug $\dim_F (H) = \dim_F (A(ωFH))$, where $ωFH$ is the augmentation ideal of the group ring $FH$. The number ${\rm{aug} \dim}...