JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 80-86.doi: 10.6040/j.issn.1671-9352.0.2019.839

Previous Articles    

Number of homomorphisms between central-dihedral group and dihedral group

XIE Wei, GUO Ji-dong*   

  1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2020-07-14

PDF (PC)

437

Abstract: Based on the group structure and element properties of central-dihedral group and dihedral group in group theory, the number of homomorphisms between central-dihedral group and dihedral group is calculated by using the related theories of algebra and number theory. As an application, the conjecture of T.Asai & T.Yoshida is proved to be valid for such groups.

Key words: central-dihedral group, homomorphism, conjecture of T.Asai &, T.Yoshida

CLC Number: 

  • O152.6
[1] FROBENIUS G. Uber einen fundamentalsatz der grouppentheorie[M] //Gesammelte Abhan-dlungen. Berlin: Springer-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 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(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(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(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] 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.
[11] 张良,海进科. 一类亚循环群同态个数的计算[J]. 吉林大学学报(理学版),2018,56(5):1045-1048. ZHANG Liang, HAI Jinke. Calculation of number of homomorphisms of a class of metacyclic groups[J]. Journal of Jilin University(Science Edition), 2018, 56(5):1045-1048.
[12] 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.
[13] 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.
[14] 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.
[15] JOHNS. A course on group theory[M]. Cambridge: Cambridge University Press, 1978.
[1] LI Hong-xia, GUO Ji-dong, HAI Jin-ke. The number of homomorphisms from dihedral groups to a class of metacyclic groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 34-40.
[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] . The number of homomorphisms from metacyclic groups to metacyclic groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 17-22.
[5] WANG Shou-feng. Prehomomorphisms and restricted products of regular semigroups with a multiplicative inverse transversal [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 90-93.
[6] 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.
[7] PENG Jia-yin. [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 119-126.
[8] HUANG Shu-liang. Several results on derivations of formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 43-46.
[9] LIU Wei-feng, DU Ying-xue, XU Hong-wei. Interval soft Boolean algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 104-110.
[10] HAO Cui-xia, YAO Bing-xue*. θ-fuzzy homomorphism of groups#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 51-56.
[11] LI Xu-dong. Stabilizer of  N(2,2,0) algebras [J]. J4, 2011, 46(8): 68-72.
[12] SU Yu, KONG Xiang-zhi*. LρC-regular semigroups [J]. J4, 2011, 46(4): 68-69.
[13] LIU Kai-Zhen, KONG Xiang-Zhi. The structure of semi-superabundant semigroups [J]. J4, 2010, 45(1): 86-88.
[14] YUAN Zhi-ling . Construction of regular semigroups with orthodox transversals [J]. J4, 2008, 43(8): 35-37 .
[15] DING Yue . H#-abundant semi-groups [J]. J4, 2008, 43(4): 55-57 .
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