JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 31-34.doi: 10.6040/j.issn.1671-9352.0.2022.305

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The number of homomorphisms from dihedral groups to any finite groups

Jie TAN1(),Liang ZHANG1,2,*(),Jidong GUO1,2   

  1. 1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Received:2022-05-30 Online:2023-06-20 Published:2023-05-23
  • Contact: Liang ZHANG E-mail:1115120694@qq.com;zhangliang0819@aliyun.com

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Abstract:

Automorphism groups and normal subgroups of dihedral groups are studied, and the number of homomorphisms from dihedral groups to any finite group is obtained. As an application of this result, the conjecture of Asai and Yoshida is verified for dihedral groups.

Key words: dihedral group, the number of homomorphisms, automorphism group

CLC Number: 

  • O152.1
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