Number of Sylow subgroups in finite groups

2017/09/01 by Guo, Wenbin, Vdovin, Evgeny
#20D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1709.00148

Abstract

Denote by ν_p(G) the number of Sylow p-subgroups of G. It is not difficult to see that ν_p(H)≤ν_p(G) for H≤ G, however ν_p(H) does not divide ν_p(G) in general. In this paper we reduce the question whether ν_p(H) divides ν_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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