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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 30-36.doi: 10.6040/j.issn.1671-9352.0.2020.007

• • 上一篇    

一类非交换群与二面体群之间的同态个数

赖吉娜,郭继东*   

  1. 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:赖吉娜(1995— ), 女, 硕士研究生, 研究方向为群论. E-mail:1048028355@qq.com*通信作者简介:郭继东(1965— ), 男, 教授, 研究方向为群论. E-mail:guojd662@163.com
  • 基金资助:
    新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2020I018)

Number of homomorphisms from a class of non-abelian groups into dihedral groups

LAI Ji-na, GUO Ji-dong*   

  1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2020-12-01

摘要: 计算了一类非交换群与二面体群之间的同态个数。作为应用,验证了这2个群之间的同态个数满足T. Asai和T. Yoshida的猜想。

关键词: 非交换群, 二面体群, 群同态

Abstract: The number of homomorphisms from a class of non-abelian groups into dihedral groups is calculated. As an application, it verifies that T. Asai and T. Yoshidas conjecture is satisfied such groups.

Key words: non-abelian group, dihedral group, group homomorphism

中图分类号: 

  • O152.6
[1] YOSHIDA T. |Hom(A, G)|[J]. Journal of Algebra, 1993, 156(1):125-156.
[2] ASAI T, YOSHIDA T. |Hom(A, G)|(Ⅱ)[J]. Journal of Algebra, 1993, 160(1):273-285.
[3] ASAI T, TAKEGAHARA Y. |Hom(A, G)|(Ⅳ)[J]. Journal of Algebra, 2001, 246:543-563.
[4] RAJKUMAR R, GAYATHRI M, ANITHA T. The number of homomorphisms from dihedral group into some finite groups[J]. Mathematical Sciences International Research Journal, 2015, 4(1):161-165.
[5] RAJKUMAR R, GAYATHRI M, ANITHA T. The number of homomorphisms from quarternion group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3):23-30.
[6] RAJKUMAR R, GAYATHRI M, ANITHA T. Counting homomorphisms from quasidihedral group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3):9-13.
[7] 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 Southwest University(Natural Science), 2013, 35(10):56-59.
[8] 徐明曜. 有限群导引[M]. 北京: 科学出版社, 1999. XU Mingyao. Finite groups: an introduction[M]. Beijing: Science Press, 1999.
[9] 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. LI Hongxia, GUO Jidong, HAI Jinke. The number of homomorphisms from the dihedral group into a class of metacyclic groups[J]. Journal of Shandong University(Natural Science), 2019, 54(6):34-40.
[10] ROSE J S. A course on group theory[M]. Cambridge: Cambridge University Press, 1978.
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