Periodic Linear Groups with the Weak Chain Conditions on Subgroups of Infinite Central Dimension

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. (2004) and Kurdachenko and Subbotin (2006), 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.