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arXiv · 2110.08852

The Fitting height is bounded by a function of the exponent

Francesco Fumagalli·Felix Leinen·Orazio Puglisi
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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 by Shalev.

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Francesco Fumagalli, Felix Leinen, Orazio Puglisi. 2021-10-17. The Fitting height is bounded by a function of the exponent. https://arxiv.org/abs/2110.08852

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