Linear groups with minimality condition for some infinite-dimensional subgroups

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 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. © 2005 Springer Science+Business Media, Inc.