The Fitting height is bounded by a function of the exponent
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08852
 Bibcode:
 2021arXiv211008852F
 Keywords:

 Mathematics  Group Theory;
 20D10;
 20D25;
 20D30