Fitting height and lengths of laws in finite solvable groups

2023/04/10 by Leinen, Felix, Puglisi, Orazio
#20E34 #20F05 #20F16 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2304.04466

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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