Linear groups with minimality condition for some infinite-dimensional subgroups

  • M. R. Dixon
  • M. J. Evans
  • L. A. Kurdachenko

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.
Published
25.11.2005
How to Cite
DixonM. R., EvansM. J., and KurdachenkoL. A. “Linear Groups With Minimality Condition for Some Infinite-Dimensional Subgroups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 11, Nov. 2005, pp. 1476–1489, https://umj.imath.kiev.ua/index.php/umj/article/view/3702.
Section
Research articles