### The number of homomorphisms from metacyclic groups to metacyclic groups

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
• Received:2017-10-31 Online:2018-06-20 Published:2018-06-13

Abstract: The number of homomorphisms between a class of metacyclic groups, which are normal cyclic groups of the order m extended by cyclic groups of the order 2p, is calculated, and the number of endomorphisms of such groups is obtained. As an application, the number of homomorphisms of such groups satisfies the conjecture of T.Asai and T.Yohsdia is varified.

CLC Number:

• O152.6
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