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