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The composition and derived lengths of a soluble group. (English) Zbl 0663.20015

The main result (Theorem 8) of this paper gives an upper bound on the derived length of a finite soluble group in terms of its composition length n. The bound is too unpleasant to state here; an approximation to it is \(\alpha\) \(log_ 2n+\beta\) where \(\alpha\) \(\doteq 2.578\) and \(\beta\) \(\doteq 8.785\).
Reviewer: M.F.Newman

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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References:

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