The number of Hall <IMG BORDER="0" SRC="/proc/2004-132-09/S0002-9939-04-07412-X/gif-title0/img1.gif" >-subgroups of a <IMG BORDER="0" SRC="/proc/2004-132-09/S0002-9939-04-07412-X/gif-title0/img2.gif" >-separable group期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The number of Hall -subgroups of a -separable group

Authors:	Alexandre Turull

Institution:	Department of Mathematics, University of Florida, Gainesville, Florida 32611-8105

Abstract:	We observe a simple formula to compute the number $\nu_\pi(G)$ of Hall $\pi$ -subgroups of a $\pi$ -separable finite group in terms of only the action of a fixed Hall $\pi$ -subgroup of on a set of normal $\pi'$ -sections of . As a consequence, we obtain that $\nu_\pi(K)$ divides $\nu_\pi(G)$ whenever is a subgroup of a finite $\pi$ -separable group . This generalizes a recent result of Navarro. In addition, our method gives an alternative proof of Navarro's result.

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