JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 45-49.doi: 10.6040/j.issn.1671-9352.0.2021.411

Previous Articles    

Number of homomorphisms between intra-commutative p-groups and quaternion groups

LIAO Qing-qing, GUO Ji-dong*, ZHANG Liang   

  1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2022-01-07

PDF (PC)

151

Abstract: Based on the group structure and element properties of intra-commutative p-groups and quaternion groups, the number of homomorphisms from a class of intra-commutative p-groups into quaternion groups is calculated. As an application, the conjecture of T.Asai and T.Yoshida is proved to be valid for such groups.

Key words: intra-commutative p-groups, quaternion 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] RAJKUMAR R, GAYATHRI M, ANITHA T. Counting homomorphisms from quasi-dihedral group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3-B):9-13.
[7] RAJKUMAR R, GAYATHRI M, ANITHA T. Enumeration of homomorphisms from modular group into some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3-B):15-19.
[8] 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.
[9] 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(3):442-448. MA Xueli, GUO Jidong, HAI Jinke. The number of homomorphisms from the quaternion group into a class of metacyclic groups[J]. Journal of Yunnan University(Natural Sciences Edition), 2019, 41(3):442-448.
[10] 李凤娇,高百俊.四元数群到一类10pn阶非交换群的同态数量[J].吉林大学学报(理学版),2020,58(5):1085-1092. LI Fengjiao, GAO Baijun. Number of homomorphisms from quaternion group to a class of non-abelian groups with order 10pn[J]. Journal of Jilin University(Science Edition), 2020, 58(5):1085-1092.
[11] 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.
[12] 闵嗣鹤,严士健. 初等数论[M]. 北京:高等教育出版社,2006. MIN Sihe, YAN Shijian. Elementary number theory[M]. Beijing: Higher Education Press, 2006.
[13] JOHNS. A course on group theory[M]. Cambridge: Cambridge University Press, 1978.
[1] 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.
[2] 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.
[3] 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.
[4] 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