JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 7-13.doi: 10.6040/j.issn.1671-9352.0.2022.209

Previous Articles     Next Articles

The number of homomorphisms between a class of finite 2-groups and dihedral groups

ZHANG Wei1,2, LAI Ji-na1,2, GUO Ji-dong1,2*, ZHANG Liang1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. Institute of applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2023-03-02

PDF (PC)

161

Abstract: Based on the group structure and element properties of G2 and dihedral groups, the number of homomorphisms between G2 and dihedral groups is calculated. As an application, it verifies that T.Asai and T.Yoshidas conjecture is satisfied such groups.

Key words: finite 2-groups, dihedral groups, group homomorphism

CLC Number: 

  • O152.6
[1] FROBENIUS G. Uber einen fundamentalsatz der grouppentheorie[M] // Gesammelte Abhandlungen. Berlin: Springer-Verlag, 1903.
[2] YOSHIDA T. |Hom(A,G)|,I[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 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 quaternion group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3-A):23-30.
[6] 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.
[7] 赖吉娜,郭继东,海进科. 一类非交换群和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. LAI Jina, GUO Jidong, HAI Jinke. The number of homomorphisms from a class of non-Abelian groups into dihedral groups[J]. Journal of shandong University(Natural Science), 2020, 55(8):80-86.
[8] JOHNSON J. The number of group homomorphisms from Dm into Dn[J]. The College Mathematics Journal, 2013, 44:190-192.
[9] 徐明曜,曲海鹏. 有限p群[M]. 北京:北京大学出版社,2010. XU Mingyao, QU Haipeng. Finite p groups[M]. Beijing: Beijing University Press, 2010.
[10] JOHNS. A course on group theory[M]. Cambridge: Cambridge University Press, 1978.
[11] SIERPINSKI, W. Elementary theory of numbers [M]. Amsterdam: North-Holand, 1988.
[1] LIAO Qing-qing, GUO Ji-dong, ZHANG Liang. Number of homomorphisms between intra-commutative p-groups and quaternion groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 45-49.
[2] LAI Ji-na, GUO Ji-dong. Number of homomorphisms from a class of non-abelian groups into dihedral groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 30-36.
[3] ZHAO Yan-wei, HAI Jin-ke. T.Asai and T.Yoshida problem of group homomorphism [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 101-105.
[4] LI Ning-ying, GUO Ji-dong, HAI Jin-ke. Number of homomorphisms between groups with Abel direct factors and finite groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 59-62.
[5] LIU Ni, ZHANG Miao-miao. Continuous directed-complete ordered semigroups and their categorical properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 57-64.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd