Fitting height and lengths of laws in finite solvable groups
Group Theory
2023-05-23 v2
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.
Cite
@article{arxiv.2304.04466,
title = {Fitting height and lengths of laws in finite solvable groups},
author = {Felix Leinen and Orazio Puglisi},
journal= {arXiv preprint arXiv:2304.04466},
year = {2023}
}
Comments
we found a gap in the proof of the main result (Theorem B)