MATHEMATICS

Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup

D. V. Gritsuk

F. Scorina Gomel State University, Gomel, Belarus

Abstract: It is proved that the derived $p$-length $l_p^a(G)$ of the $p$-solvable group $G$ in which the Sylow $p$-subgroup has order $p^n$ is at most $1+\frac n2$ and if $p\not\in\{2,3\}$ then $l_p^a(G)\leqslant\frac{n+1}2$.

Keywords: finite group, $p$-solvable group, Sylow subgroup, derived $p$-length.

UDC: 512.542

Received: 15.08.2014