2008
DOI: 10.5565/publmat_52108_07
|View full text |Cite
|
Sign up to set email alerts
|

Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension

Abstract: Let 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 /C V (G). In [DEK] and [KS], soluble linear groups in which the set L icd (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 L icd (G) satisfies one of the weak chain conditions (the weak minimal conditio… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
11
0

Year Published

2008
2008
2020
2020

Publication Types

Select...
5
1

Relationship

1
5

Authors

Journals

citations
Cited by 8 publications
(11 citation statements)
references
References 14 publications
0
11
0
Order By: Relevance
“…Let P be the Sylow p-subgroup of T (G). [15,Proposition 3.1] shows that P is bounded nilpotent. Since G is not finitary, there exists 1 = g ∈ G \ F D(G).…”
Section: Corollary 1 Let G Be a Locally Nilpotent Subgroup Of G L(v mentioning
confidence: 99%
See 3 more Smart Citations
“…Let P be the Sylow p-subgroup of T (G). [15,Proposition 3.1] shows that P is bounded nilpotent. Since G is not finitary, there exists 1 = g ∈ G \ F D(G).…”
Section: Corollary 1 Let G Be a Locally Nilpotent Subgroup Of G L(v mentioning
confidence: 99%
“…After finitely many steps, we obtain that P j /P j−1 is G-central. It follows that the factor-group G/Q is nilpotent, then it must be minimax by [15,Theorem A]. Being bounded, P is finite.…”
Section: Lemma 3 Let G Be a Torsion-free Nilpotent Minimax Group Thementioning
confidence: 99%
See 2 more Smart Citations
“…The weak minimal and the weak maximal conditions are natural group-theoretical generalization of the ordinary minimal and maximal conditions. The study of linear groups in which the family L icd (G) satisfies the weak minimal condition has been initiated in [3,7]. In the present article, we would like to offer another approach in studying of infinite dimensional groups.…”
Section: Following [2] We Say That H Has Finite Central Dimension Ifmentioning
confidence: 99%