Finite groups with some maximal subgroups of Sylow subgroups ℳ-supplemented

被引：0
作者：
Long Miao
机构：
[1] Yangzhou University,
来源：
Mathematical Notes | 2009年 / 86卷
关键词：
Sylow subgroup; ℳ-supplemented subgroup; formation; finite group; supersolvable group; Hall subgroup; Fitting subgroup; p-nilpotent group;
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摘要：
A subgroup H of a group G is said to be ℳ-supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H. In this paper, we obtain the following statement: Let ℱ be a saturated formation containing all supersolvable groups and H be a normal subgroup of G such that G/H ε ℱ. Suppose that every maximal subgroup of a noncyclic Sylow subgroup of F*(H), having no supersolvable supplement in G, is ℳ-supplemented in G. Then G ε ℱ.
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页码：655 / 664
页数：9
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