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 Dixon et al. (Citation2004) and Kurdachenko and Subbotin (Citation2006), 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. In this article we study periodic locally radical linear groups, in which the set ℒ icd(G) satisfies one of the weak chain conditions: the weak minimal condition or the weak maximal condition.
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ACKNOWLEDGMENT
The authors wish to thank the referee for his/her excellent work and useful comments that have allowed to improve the layout and the contents of this article.
This article is supported by Proyecto MTM2004-04842 of Dirección General de Investigación MEC (Spain).
Notes
Communicated by M. R. Dixon