Journal of Jilin University Science Edition ›› 2020, Vol. 58 ›› Issue (5): 1085-1092.

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Number of Homomorphisms from Quaternion Group to a Class of Non-Abelian Groups with Order 10pn

LI Fengjiao, GAO Baijun   

  1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China
  • Received:2020-01-06 Online:2020-09-26 Published:2020-11-18

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Abstract: By using the finite group theory and elementary number theory, we ascertained the characteristics of elements of a class of non-Abelian finite group with order 10pn, and built all homomorphic mappings from quaternion group to the class of non-Abelian finite group with order 10pn. We verified that those two groups could suffice the conjecture of Asai and Yoshida by calculating the number of homomorphic mapping.

Key words: non-Abelian group, quaternion group, number of homomorphisms

CLC Number: 

  • O152.6
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