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

Leonid A. Kurdachenko, José M. Muñoz-Escolano, and Javier Otal

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Abstract

Let $V$ be a vector space over a field $F$. If $G\!\leq\! GL(V,F)$, 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 $\mathcal{L}_{\operatorname{icd}}(G)$ 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 $\mathcal{L}_{\operatorname{icd}}(G)$ 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 $\mathcal{L}_{\operatorname{icd}}(G)$ satisfies one of the two weak chain conditions.

Article information

Source
Publ. Mat., Volume 52, Number 1 (2008), 151-169.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.pm/1197908700

Mathematical Reviews number (MathSciNet)
MR2384844

Zentralblatt MATH identifier
1149.20030

Subjects
Primary: 20F22: Other classes of groups defined by subgroup chains
Secondary: 20H20: Other matrix groups over fields

Keywords
Locally nilpotent group linear group central dimension of a linear group weak minimal condition weak maximal condition

Citation

Kurdachenko, Leonid A.; Muñoz-Escolano, José M.; Otal, Javier. Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension. Publ. Mat. 52 (2008), no. 1, 151--169. https://projecteuclid.org/euclid.pm/1197908700


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