The Upper Central Series in Linear Groups
In  M.S. Garaščuk proves that every locally nilpotent linear group is hypercentral. K.W. Gruenberg () gave another proof of this and, amongst other things, proved that the Fitting subgroup of a linear group is nilpotent and that the central height of a linear group is less than 2ω. In  he sharpened the latter result; there exists an integer-valued function ψ(n) such that if G is any subgroup of GL(n, F) then G has central height at most ω + ψ(n). This bound is reduced in , the correct bound being given for the locally nilpotent case. Chapter 8 consists of an exposition of the results of these papers together with some related theorems (on the size of the upper central factors of a linear group) and examples.
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