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2008 Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension
Leonid A. Kurdachenko, José M. Muñoz-Escolano, Javier Otal
Publ. Mat. 52(1): 151-169 (2008).

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.

Citation

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Leonid A. Kurdachenko. José M. Muñoz-Escolano. Javier Otal. "Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension." Publ. Mat. 52 (1) 151 - 169, 2008.

Information

Published: 2008
First available in Project Euclid: 17 December 2007

zbMATH: 1149.20030
MathSciNet: MR2384844

Subjects:
Primary: 20F22
Secondary: 20H20

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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