Abstract
Every finite solvable group G has a normal series with nilpotent factors. The smallest possible number of factors in such a series is called the Fitting height h(G). In the present paper, we derive an upper bound for h(G) in terms of the exponent of G. Our bound constitutes a considerable improvement of an earlier bound obtained in Shalev (Proc Am Math Soc 126(12):3495–3499, 1998).
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