JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 34-40.doi: 10.6040/j.issn.1671-9352.0.2018.362

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The number of homomorphisms from dihedral groups to a class of metacyclic groups

LI Hong-xia1, GUO Ji-dong1*, HAI Jin-ke1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2019-06-05

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Abstract: Based on the theory group of the structure of metacyclic group and characteristics of the group elements, by using the basic method of algebra and number theory, it is calculated that the number of homomorphism between dihedral groups and a class of metacyclic groups. As an application, it verifies that T.Asai and T.Yoshidas conjectures establish such a cyclic group.

Key words: dihedral group, metacyclic group, homomorphism

CLC Number: 

  • O152.6
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