关于Sylow p-子群的极大子群的$\mathscr{F}$-可补性对群结构的影响

doi:10.6040/j.issn.1671-9352.0.2023.047

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (6): 98-102.doi: 10.6040/j.issn.1671-9352.0.2023.047

关于Sylow p-子群的极大子群的$\mathscr{F}$-可补性对群结构的影响

高百俊¹(),汤菊萍²,高志超^3,*(),宋菊⁴

1. 伊犁师范大学数学与统计学院, 新疆伊宁 835000
2. 无锡职业技术学院基础课部, 江苏无锡 214121
3. 华中师范大学数学与统计学院, 湖北武汉 430079
4. 扬州大学数学科学学院, 江苏扬州 225002

收稿日期:2023-02-14 出版日期:2024-06-20 发布日期:2024-06-17
通讯作者: 高志超 E-mail:dqgbj2008@163.com;1102576920@qq.com
作者简介:高百俊(1980—), 女, 教授, 博士, 研究方向为有限群论. E-mail: dqgbj2008@163.com
基金资助:
国家自然科学基金资助项目(12371018);国家自然科学基金资助项目(11701223);江苏省高等学校基础科学(自然科学)研究项目(22KJB110024);新疆维吾尔自治区天山青年计划资助项目(2020Q023);伊犁师范大学提升学科综合实力专项自科一般项目(22xkzy19)

Influence of $\mathscr{F}$-supplemented property of maximal subgroups of Sylow p-subgroup on the structure of groups

Baijun GAO¹(),Juping TANG²,Zhichao GAO^3,*(),Ju SONG⁴

1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
2. Department of Fundamental Courses, Wuxi Institute of Technology, Wuxi 214121, Jiangsu, China
3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China
4. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, Jiangsu, China

Received:2023-02-14 Online:2024-06-20 Published:2024-06-17
Contact: Zhichao GAO E-mail:dqgbj2008@163.com;1102576920@qq.com

摘要/Abstract

摘要：

结合群类理论, 将群类$S_{p}^{*}$拓展到群类$S_{p^{2}}^{*}$和$S_{p^{3}}^{*}$, 并由此定义$S_{p^{*} i}^{*}$可补子群, $i=1, 2, 3$。进一步利用Sylow $p$-子群的极大子群的$S_{p^i}^{*}$-可补性质研究广义$p$-可解群的构造。

关键词: Sylow p-子群, 极大子群, 可补子群, 广义p-可解群

Abstract:

Using the theory of group classes, the group classes $S_{p^{2}}^{*}$ and $S_{p^{3}}^{*}$ are obtained by generalizing the group class $S_{p}^{*}$, and $S_{p^i}^{*}$-supplemented subgroups are defined, where $i=1, 2, 3$. Furthermore, the structure of generalized $p$-solvable groups is studied by using $S_{p^{i}}^{*}$-supplemented property of maximal subgroups of Sylow $p$-subgroup.

Key words: Sylow p-subgroup, maximal subgroup, supplemented subgroup, generalized p-solvable group

中图分类号:

O152.1

高百俊,汤菊萍,高志超,宋菊. 关于Sylow p-子群的极大子群的$\mathscr{F}$-可补性对群结构的影响[J]. 《山东大学学报(理学版)》, 2024, 59(6): 98-102.

Baijun GAO,Juping TANG,Zhichao GAO,Ju SONG. Influence of $\mathscr{F}$-supplemented property of maximal subgroups of Sylow p-subgroup on the structure of groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 98-102.

参考文献 18

1	GUO Wenbin . The theory of classes of groups[M]. Boston: Kluwer Academic Publishers, 2000.
2	HUPPERT B , BLACKBURN N . Finite groups Ⅲ[M]. New York: Springer-Verlag, 1982.
3	ARAD Z , WARD M B . New criteria for the solvability of finite groups[J]. Journal of Algebra, 1982, 77 (1): 234- 246. doi: 10.1016/0021-8693(82)90288-5
4	WANG Yanming . Finite groups with some subgroups of Sylow subgroups c-supplemented[J]. Journal of Algebra, 2000, 224 (2): 467- 478. doi: 10.1006/jabr.1999.8079
5	QIAN Guohua . Finite groups whose maximal subgroups of Sylow p-subgroups admit a p-solvable supplement[J]. Science China Mathematics, 2013, 56 (5): 1015- 1018. doi: 10.1007/s11425-012-4485-9
6	MIAO Long , LEMPKEN W . On $\mathscr{M}$-supplemented subgroups of finite groups[J]. Journal of Group Theory, 2009, 12 (2): 271- 287.
7	BALLESTER-BOLINCHES A , GUO X Y . On complemented subgroups of finite groups[J]. Archiv Der Mathematik, 1999, 72 (3): 161- 166. doi: 10.1007/s000130050317
8	MONAKHOV V S , TROFIMUK A A . On the supersolubility of a finite group with NS-supplemented subgroups[J]. Acta Mathematica Hungarica, 2020, 160 (1): 161- 167. doi: 10.1007/s10474-019-00997-4
9	MONAKHOV V S , KNIAHINA V N . Finite groups with complemented subgroups of prime orders[J]. Journal of Group Theory, 2015, 18 (6): 905- 912. doi: 10.1515/jgth-2015-0023
10	MIAO Long , TANG Juping . A new condition for solvable groups[J]. Journal of Pure and Applied Algebra, 2017, 221 (10): 2504- 2510. doi: 10.1016/j.jpaa.2016.12.035
11	ZHANG Jia , QIU Tingting , MIAO Long , et al. Notes on solvability and p-supersolvability of finite groups[J]. Algebra Colloquium, 2019, 26 (1): 139- 146. doi: 10.1142/S1005386719000130
12	ZHANG Jia , MIAO Long , BAO Hongwei . On nearly $\mathscr{M}$-supplemented primary subgroups of finite groups[J]. Communications in Algebra, 2019, 47 (2): 896- 903. doi: 10.1080/00927872.2018.1498868
13	DONG Shuqin , QIU Tingting , GAO Zhichao , et al. A generalization of Skiba's problem[J]. Publicationes Mathematicae Debrecen, 2022, 100 (1/2): 1- 10.
14	DONG Shuqin , MIAO Long , GAO Baijun . On weakly $\mathscr{M}$-supplemented subgroups of finite groups[J]. Communications in Algebra, 2021, 49 (9): 4021- 4027. doi: 10.1080/00927872.2021.1910701
15	GAO Zhichao , LI Jinbao , MIAO Long . On CAP_{S_p^*}-subgroups of finite groups[J]. Communications in Algebra, 2021, 49 (3): 1120- 1127. doi: 10.1080/00927872.2020.1828443
16	GUO W B , SHUM K P , SKIBA A N . G-covering subgroup systems for the classes of supersoluble and nilpotent groups[J]. Israel Journal of Mathematics, 2003, 138 (1): 125- 138. doi: 10.1007/BF02783422
17	ISAACS I M . Finite group theory[M]. Providence: American Mathematical Society, 2008.
18	KURZWEIL H , STELLMACHER B . The theory of finite groups: an introduction[M]. New York: Springer, 2004.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

[1]	曹建基,王俊新,白鹏飞. 蕴含交换极大子群的极大类3-群上的光滑斜态射[J]. 《山东大学学报(理学版)》, 2024, 59(4): 23-30.
[2]	陈心丹,许丽,缪龙,刘威. 有限群的2-极大子群的边界因子[J]. 《山东大学学报(理学版)》, 2023, 58(2): 1-5.
[3]	史江涛,任惠瑄. 关于非幂零极大子群皆正规的有限群具有Sylow塔的注记[J]. 《山东大学学报(理学版)》, 2021, 56(8): 58-60.
[4]	刘鑫,吴珍凤,杨南迎. 有限群的m-S-可补子群[J]. 《山东大学学报(理学版)》, 2021, 56(4): 8-13.
[5]	毛月梅,杨南迎. 有限群的p-幂零性和超可解性[J]. 山东大学学报（理学版）, 2016, 51(4): 39-42.
[6]	高辉,高胜哲*,尹丽. 子群的θ-完备和群的结构[J]. 山东大学学报（理学版）, 2014, 49(03): 43-45.
[7]	高辉，高胜哲，尹丽. 关于极大子群的θ-偶[J]. J4, 2011, 46(2): 97-100.
[8]	普昭年1,汤菊萍2,顾春华3. 局部子群的性质对群构造的影响[J]. J4, 2011, 46(12): 51-54.
[9]	王俊新. 几则有限群可解的条件[J]. J4, 2009, 44(8): 35-38.

关于Sylow p-子群的极大子群的$\mathscr{F}$-可补性对群结构的影响

Influence of $\mathscr{F}$-supplemented property of maximal subgroups of Sylow p-subgroup on the structure of groups

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献 18

相关文章 9

多维度评价

本文评价

推荐阅读 10