Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension
Kurdachenko, Leonid A. (University of Dnepropetrovsk (Ucraïna). Department of Algebra)
Múñoz-Escolano, José M. (Universidad de Zaragoza. Departamento de Matemáticas)
Otal, Javier (Universidad de Zaragoza. Departamento de Matemáticas)

Data: 2008
Resum: 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/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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Locally nilpotent group ; Linear group ; Central dimension of a linear group ; Weak minimal condition ; Weak maximal condition
Publicat a: Publicacions Matemàtiques, V. 52 n. 1 (2008) p. 151-169, ISSN 0214-1493

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_52108_07
DOI: 10.5565/PUBLMAT_52108_07
DOI: 10.5565/74468

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