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arXiv · 2304.04466

Fitting height and lengths of laws in finite solvable groups

Felix Leinen·Orazio Puglisi
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Abstract

Let G be a finite solvable group, and let h(G) denote its Fitting height, namely the length of a shortest normal series in G with nilpotent factors. We show, that any law in G has length at least h(G). This result is then used to improve a previously given bound on the nonsolvable length of finite nonsolvable groups.

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Felix Leinen, Orazio Puglisi. 2023-04-10. Fitting height and lengths of laws in finite solvable groups. https://arxiv.org/abs/2304.04466

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