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 e-prints
- Pub Date:
- October 2021
- arXiv:
- arXiv:2110.08852
- Bibcode:
- 2021arXiv211008852F
- Keywords:
-
- Mathematics - Group Theory;
- 20D10;
- 20D25;
- 20D30