| Sylow子群的极大子群皆s-半正规的有限群 |
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| 引用本文： | 王坤仁. Sylow子群的极大子群皆s-半正规的有限群[J]. 四川师范大学学报(自然科学版), 2005, 28(3): 253-255 |
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| 作者姓名： | 王坤仁 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 四川省学位委员会资助项目，四川省教育厅资助项目 |
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| 摘 要： | 子群H称为在有限群G中s 半正规,若H同G的所有阶互素于｜H｜的Sylow子群可换.主要结果如下:有限群G的所有Sylow子群及其极大子群都在G中s 半正规的充要条件是G的所有阶互素的Sylow子群之极大子群互相可换并且G的每个主因子H/R是素数阶的,若｜H/R｜=p,则｜G/CG(H/R) ｜=qb,其中素数q使qb 整除p- 1 .
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| 关 键 词： | s-半正规 极大子群 Sylow子群 超可解性 |
Finite Groups Whose Maximal Subgroups of Sylow Subgroups are s-seminormal |
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| WANG Kun-ren. Finite Groups Whose Maximal Subgroups of Sylow Subgroups are s-seminormal[J]. Journal of Sichuan Normal University(Natural Science), 2005, 28(3): 253-255 |
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| Authors: | WANG Kun-ren |
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| Abstract: | A subgroup H of a finite group G is called s-seminormal in G if H permutes with all Sylow subgroups of G with order prime to |H|. In this paper, the structure of finite groups G with maximal subgroups of Sylow subgroups s-seminormal in G is determined:G is a group with s-seminormal Sylow subgroups and s-seminormal maximal subgroups of Sylow subgroups if and only if all maximal subgroups of Sylow subgroups of G with coprime order permute each other and each chief factor H/R of G is of prime order, moreover, if |H/R|=p then |G/C_G(H/R)|=q~b, where q is a prime and q~b divides p-1. |
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| Keywords: | s-seminormal Maximal subgroup Sylow subgroup Supersolvable |
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