具有非交换Sylow子群的p2q3阶群的构造

doi:10.6040/j.issn.1671-9352.0.2014.502

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (12): 93-97.doi: 10.6040/j.issn.1671-9352.0.2014.502

具有非交换Sylow子群的p²q³阶群的构造

陈松良^1,2

1. 贵州师范学院数学与计算机科学学院, 贵州贵阳 550018;
2. 贵州省高校工业物联网工程技术研究中心, 贵州贵阳 550018

收稿日期:2014-11-10 修回日期:2015-06-01 出版日期:2015-12-20 发布日期:2015-12-23
作者简介:陈松良(1964-),男,博士,教授,研究方向为有限群论.E-mail:chsl_20136@aliyun.com
基金资助:
贵州省自然科学基金资助项目([2012]2289,[2013]2234);贵阳市科技计划项目(筑科合同[2013101]10-6)

On the structures of groups of order p²q³ with non-Abelian Sylow subgroups

CHEN Song-liang^1,2

1. School of Mathematics and Computer Science, Guizhou Normal College, Guiyang 550018, Guizhou, China;
2. Industrial Internet of Things Engineering Research Center, Higher Education Institutions of Guizhou Province, Guiyang 550018, Guizhou, China

Received:2014-11-10 Revised:2015-06-01 Online:2015-12-20 Published:2015-12-23

摘要/Abstract

摘要： 设p,q为奇素数,且p>q,而G是Sylow q-子群非交换的p²q³阶群。利用有限群的局部分析方法,对G进行了完全分类并获得了其全部构造。

关键词: 有限群, 同构分类, 群的构造

Abstract: Let p, q be odd primes such that p>q, and G be groups of order p²q³ with non-Abelian Sylow q-subgroups. The isomorphic classification of G and their structures are determined with the help of local analysis of finite groups.

Key words: isomorphic classification, finite group, structure of group

中图分类号:

O152.1

陈松良. 具有非交换Sylow子群的p²q³阶群的构造[J]. 山东大学学报（理学版）, 2015, 50(12): 93-97.

CHEN Song-liang. On the structures of groups of order p²q³ with non-Abelian Sylow subgroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 93-97.

参考文献

[1] 陈松良. 论Sylow p-子群循环的pⁿq³阶群的构造[J]. 东北师范大学学报:自然科学版,2013,45(2):35-38. CHEN Songliang. On the structures of groups of order pⁿq³ with cyclic Sylow p-subgroups[J]. Journal of Northeast Normal University: Natural Science Edition, 2013, 45(2): 35-38.
[2] 陈松良. 关于Sylow子群皆交换的p²q³阶群的构造[J]. 武汉大学学报:理学版,2013,59(3):295-300. CHEN Songliang. On the structures of groups of order p²q³ with Abelian Sylow subgroups[J]. Journal of Wuhan University: Natural Science Edition, 2013, 59(3):295-300.
[3] 徐明曜. 有限群导引:上册[M]. 北京:科学出版社,1999. XU Mingyao. Introduction to finite group: Vol. 1[M]. Beijing: Science Press, 1999.
[4] ROBINSON D J S. A course in the theory of groups[M]// Graduate Texts in Mathematics 80. New York: Springer-Verlag, 1982.
[5] KURZWEIL H, STELLMACHER B. The theory of finite groups[M]. New York: Springer-Verlag, 2004.
[6] HUPPERT B. Endliche gruppen I[M]. Berlin: Springer-Verlag, 1967.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

具有非交换Sylow子群的p²q³阶群的构造

On the structures of groups of order p²q³ with non-Abelian Sylow subgroups

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

多维度评价

本文评价

推荐阅读 0

[1]	陈松良,李惊雷,欧阳建新. 论p3q阶群的构造[J]. J4, 2013, 48(2): 27-31.
[2]	刘晓蕾. 关于E.Alemany等人的一个定理的一个注记[J]. J4, 2012, 47(10): 7-13.
[3]	刘晓蕾王燕鸣. 有限群中的q-补及其应用[J]. J4, 2009, 44(10): 87-90.
[4]	刘晓蕾 . 关于有限群的c-正规性的几点注记[J]. J4, 2008, 43(10): 18-20 .