Revistes Catalanes amb Accés Obert (RACO)

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

L. A. Kurdachenko, J. M. Múñoz-Escolano, J. Otal


Let $V$ be a vector space over a field $F$. If $G \leq GL(V,F)$, \emph{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.

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