A bound on the p-length of p-solvable groups

Jon Gonzalez-Sanchez, Francesca Spagnuolo

Let G be a finite p-solvable group and P a Sylow p-subgroup of G. Suppose that ${\gamma }_{l(p-1)}(P)\subseteq {\gamma }_r(P{)}^{p^s}$ for $l(p-1)<r+s(p-1)$, then the p-length is bounded by a functi…