Linear groups with minimality condition for some infinite-dimensional subgroups

Abstract

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 ${\rm{aug} \dim}_F (H)$ is called the augmentation dimension of the subgroup $H$. In the present paper, we study locally solvable linear groups with minimality condition for subgroups of infinite augmentation dimension.