两类非交换群之间的同态数量

doi:10.6040/j.issn.1671-9352.0.2020.030

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 25-29.doi: 10.6040/j.issn.1671-9352.0.2020.030

• • 上一篇

两类非交换群之间的同态数量

李凤娇,高百俊^*

伊犁师范大学数学与统计学院, 新疆伊宁 835000

发布日期:2020-12-01
作者简介:李凤娇(1995— ),女,硕士研究生,研究方向为有限群论. E-mail:1483295119@qq.com*通信作者简介:高百俊(1980— ),女,博士,副教授,研究方向为有限群论. E-mail:dqgbj2008@163.com
基金资助:
新疆维吾尔自治区自然科学基金资助项目(2017D01C419)

Number of homomorphisms between two classes of non-abelian finite groups

LI Feng-jiao, GAO Bai-jun^*

College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China

Published:2020-12-01

摘要/Abstract

摘要： 结合代数数论的知识,计算了一类 Sylow p-子群为循环群的10pⁿ阶非交换群之间的同态个数,以及这类群到四元数群的同态个数。作为应用,验证了这两类群是满足Asai和Yoshida猜想的。

关键词: 非交换群, 同态数量, 四元数群

Abstract: The number of homomorphisms among a class of non-abelian groups of order 10pⁿ with cyclic Sylow p-subgroups and from the non-abelian finite groups into quaternion group is obtained by using algebraic number theory. As an application, the number of homomorphisms of such groups satisfies the conjecture of Asai and Yoshida is verified.

Key words: non-abelian group, number of homomorphism, quaternion group

中图分类号:

O152.6

李凤娇,高百俊. 两类非交换群之间的同态数量[J]. 《山东大学学报(理学版)》, 2020, 55(12): 25-29.

LI Feng-jiao, GAO Bai-jun. Number of homomorphisms between two classes of non-abelian finite groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 25-29.

参考文献

[1] FROBENIUS G. Über einen fundamentalsatz der gruppentheorie[M] //Gesammelte Abhandlungen. Berlin: Spring-Verlag, 1903: 330-334.
[2] YOSHIDA T. |Hom(A,G)|[J]. Journal of Algebra, 1993, 156(1):125-156.
[3] ASAI T, YOSHIDA T. |Hom(A,G)|(Ⅱ)[J]. Journal of Algebra, 1993, 160(1):273-285.
[4] RAJKUMAR R, GAYATHRI M, ANITHA T. The number of homomorphisms from quaternion group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3):23-30.
[5] 马雪丽,郭继东,海进科.四元数群到一类亚循环群之间的同态个数[J].云南大学学报(自然科学版),2019,41(2):1-7. MA Xueli, GUO Jidong, HAI Jinke. The number of homomorphisms from quaternion group into a class of metacyclic groups[J]. Journal of Yunnan University(Natural Science), 2019, 41(2):1-7.
[6] 郝延芹,海进科.Asai 和Yoshida猜想的一个注记[J]. 吉林大学学报(理学版),2017,55(6):1473-1476. HAO Yanqin, HAI Jinke. A note on conjecture of Asai and Yoshida[J]. Journal of Jilin University(Science Edition), 2017, 55(6):1473-1476.
[7] 张良,海进科.亚循环群到亚循环群之间的同态个数[J].山东大学学报(理学版),2018,53(6):17-22. ZHANG Liang, HAI Jinke. The number of homomorphisms from metacyclic groups to metacyclic groups[J]. Journal of Shandong University(Natural Science), 2018, 53(6):17-22.
[8] 吉晓娟,周伟.Sylow p-子群为循环群的10pⁿ阶非交换群的非交换图[J].西南大学学报(自然科学版),2013, 35(10):56-59. JI Xiaojuan, ZHOU Wei. The non-commuting graph of non-abelian group of order 10pⁿ with cyclic sylow p-subgroups[J]. Journal of Xinan University(Natural Science), 2013, 35(10):56-59.
[9] ROSE J S. A course on group theroy[M]. Cambridge: Cambridge University Press, 1978.
[10] 闵嗣鹤,严士健.初等数论[M].3版.北京:高等教育出版社,2003. MIN Sihe, YAN Shijian. Elementary number theory[M]. 3rd ed. Beijing: Higher Education Press, 2003.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

两类非交换群之间的同态数量

Number of homomorphisms between two classes of non-abelian finite groups

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

多维度评价

本文评价

推荐阅读 0

[1]	张良,海进科. 亚循环群到亚循环群之间的同态个数[J]. 山东大学学报（理学版）, 2018, 53(6): 17-22.
[2]	赵文英,海进科. 关于有限内幂零群和Frobenius群的Coleman自同构[J]. 山东大学学报（理学版）, 2017, 52(10): 4-6.
[3]	海进科,王伟,何威萍. 关于有限群Coleman自同构的一个注记[J]. 山东大学学报（理学版）, 2016, 51(4): 35-38.
[4]	曹勇 . 关于线性变换正则序半群的BQ性[J]. J4, 2008, 43(2): 98-100 .
[5]	李红霞,郭继东,海进科. 二面体群到一类亚循环群之间的同态个数[J]. 《山东大学学报(理学版)》, 2019, 54(6): 34-40.
[6]	谢伟,郭继东. 中心二面体群与二面体群之间的同态个数[J]. 《山东大学学报(理学版)》, 2020, 55(8): 80-86.
[7]	赵乐乐,海进科. 具有某种扩张的有限群的Coleman自同构[J]. 《山东大学学报(理学版)》, 2019, 54(10): 109-112.