Add to ORKGLet V be a vector space over a field F. If G≤GL(V, F), the central dimension of G is the F-dimension of the vector space V/CV (G). In [DEK] and [KS], soluble linear groups in which the set Licd(G) of all proper infinite central dimensional subgroups of G satisfies the minimal condition and the maximal condition, respectively, have been described. On the other hand, in [MOS], periodic locally radical linear groups in which Licd(G) satisfies one of the weak chain conditions (the weak minimal condition or the weak maximal condition) have been characterized. In this paper, we begin the study of the non-periodic case by describing locally nilpotent linear groups in which Licd(G) satisfies one of the two weak chain conditions
Let F be a field, A be a vector space over F and G be a subgroup of GL(F,A). We say that G has a den...
This paper deals with one of the ways of studying infinite groups many of whose subgroups have a pre...
The $c$-dimension of a group is the maximum length of a chain of nested centralizers. It is proved t...
Let V be a vector space over a field F. If G≤GL(V, F), the central dimension of G is the F-dimension...
AbstractThe authors investigate the structure of locally soluble-by-finite groups that satisfy the w...
Let A a vector space over a field F and let H be a subgroup of GL(F, A). We define centdimF H to be di...
We describe locally (soluble-by-finite) groups in which the set of all subgroups with infinitely man...
AbstractLet GL(n,F) denote the general linear group over a commutative field F. It is well known tha...
The aim of this paper is to investigate groups whose proper subgroups are linear. Although there exi...
AbstractThe authors study infinite dimensional linear groups with the minimal condition on subgroups...
AbstractA group G is said to satisfy max-∞ if each nonempty set of infinite subgroups of G has a max...
summary:Let $G$ be a group with the property that there are no infinite descending chains of non-sub...
AbstractWe study nilpotence properties (upper central series, Engel elements, central heights, etc.)...
A group is locally finite if every finite subset generates a finite subgroup. A group of linear tran...
AbstractJ.D. Dixon has characterized those pairs (n,F), where n is a positive integer and F a field,...
Let F be a field, A be a vector space over F and G be a subgroup of GL(F,A). We say that G has a den...
This paper deals with one of the ways of studying infinite groups many of whose subgroups have a pre...
The $c$-dimension of a group is the maximum length of a chain of nested centralizers. It is proved t...
Let V be a vector space over a field F. If G≤GL(V, F), the central dimension of G is the F-dimension...
AbstractThe authors investigate the structure of locally soluble-by-finite groups that satisfy the w...
Let A a vector space over a field F and let H be a subgroup of GL(F, A). We define centdimF H to be di...
We describe locally (soluble-by-finite) groups in which the set of all subgroups with infinitely man...
AbstractLet GL(n,F) denote the general linear group over a commutative field F. It is well known tha...
The aim of this paper is to investigate groups whose proper subgroups are linear. Although there exi...
AbstractThe authors study infinite dimensional linear groups with the minimal condition on subgroups...
AbstractA group G is said to satisfy max-∞ if each nonempty set of infinite subgroups of G has a max...
summary:Let $G$ be a group with the property that there are no infinite descending chains of non-sub...
AbstractWe study nilpotence properties (upper central series, Engel elements, central heights, etc.)...
A group is locally finite if every finite subset generates a finite subgroup. A group of linear tran...
AbstractJ.D. Dixon has characterized those pairs (n,F), where n is a positive integer and F a field,...
Let F be a field, A be a vector space over F and G be a subgroup of GL(F,A). We say that G has a den...
This paper deals with one of the ways of studying infinite groups many of whose subgroups have a pre...
The $c$-dimension of a group is the maximum length of a chain of nested centralizers. It is proved t...