The shape of solvable groups with odd order

Abstract

We prove that the minimal composition length, $c$, of a solvable group with solvable length $d$ satisfies $9^{(d-3)/9}<c<9^{(d+1)/5}$, and the minimal composition length, $c^o$, of a group with odd order and solvable length $d$ satisfies $7^{(d-2)/5}<c^o<2^d$.

Added to arXiv in 2018

References in corpus (1)

• Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators