The shape of solvable groups with odd order

الأصل · EN

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, cᵒ, of a group with odd order and solvable length d satisfies 7⁽ᵈ⁻²⁾/⁵< cᵒ< 2ᵈ.