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 $7^{(d-2)/5}< c^o< 2^d$.