LAUSR

Abstract Denote by νp⁢(G){\nu_{p}(G)} the number of Sylow p-subgroups of G. It is not difficult to see that νp⁢(H)⩽νp⁢(G){\nu_{p}(H)\leqslant\nu_{p}(G)} for H⩽G{H\leqslant G}, however νp⁢(H){\nu_{p}(H)} does not divide νp⁢(G){\nu_{p}(G)} in general. In this paper we reduce the question whether νp⁢(H){\nu_{p}(H)} divides νp⁢(G){\nu_{p}(G)} for every H⩽G{H\leqslant G} to almost simple groups. This result substantially generalizes the previous result by G. Navarro and also provides an alternative proof of Navarro’s theorem.