Currently displaying 1 – 6 of 6

Showing per page

Order by Relevance | Title | Year of publication

Infinite dimensional linear groups with a large family of G -invariant subspaces

L. A. KurdachenkoA. V. SadovnichenkoI. Ya. Subbotin — 2010

Commentationes Mathematicae Universitatis Carolinae

Let F be a field, A be a vector space over F , GL ( F , A ) be the group of all automorphisms of the vector space A . A subspace B is called almost G -invariant, if dim F ( B / Core G ( B ) ) is finite. In the current article, we begin the study of those subgroups G of GL ( F , A ) for which every subspace of A is almost G -invariant. More precisely, we consider the case when G is a periodic group. We prove that in this case A includes a G -invariant subspace B of finite codimension whose subspaces are G -invariant.

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

L. A. KurdachenkoI. Ya. SubbotinT. I. Ermolkevich — 2013

Mathematica Bohemica

The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let G be a locally generalized radical...

Page 1

Download Results (CSV)