Number of Sylow subgroups in finite groups

Wenbin Guo, Evgeny Vdovin

Denote by ${\nu }_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that ${\nu }_p(H)\le {\nu }_p(G)$ for $H\le G$, however ${\nu }_p(H)$ does not divide ${\nu }_p(G)$ in general.…