Number of Sylow subgroups in finite groups

Wenbin Guo; Evgeny Vdovin

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arXiv · 1709.00148

Number of Sylow subgroups in finite groups

Wenbin Guo·Evgeny Vdovin

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Abstract

Denote by $ν_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $ν_p(H)\leqν_p(G)$ for $H\leq G$, 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 $H\leq G$ 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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BibTeX RIS

Wenbin Guo, Evgeny Vdovin. 2017-09-01. Number of Sylow subgroups in finite groups. https://arxiv.org/abs/1709.00148

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