%A LI Hong-xia, GUO Ji-dong, HAI Jin-ke %T The number of homomorphisms from dihedral groups to a class of metacyclic groups %0 Journal Article %D 2019 %J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) %R 10.6040/j.issn.1671-9352.0.2018.362 %P 34-40 %V 54 %N 6 %U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3093.shtml} %8 %X 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.