一类亚循环群同态个数的计算

Journal of Jilin University Science Edition ›› 2018, Vol. 56 ›› Issue (5): 1045-1048.

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Calculation of Number of Homomorphisms of a Class of Metacyclic Groups#br#

ZHANG Liang¹, HAI Jinke²

1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China；
2. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong Province, China

Received:2017-11-01 Online:2018-09-26 Published:2018-11-22

Abstract

Abstract: By using the group theory and congruence theory, we calculated the number of homomorphisms between a class of metacyclic groups, which were normal cyclic groups of the order m expanded by cyclic groups of the order 4, and gave the number of endomorphisms of the metacyclic groups. The results verified that the metacyclic groups satisfied the conjecture of Asai and Yoshida.

Key words: metacyclic group, homomorphism, endomorphism, congruence

CLC Number:

O152.1

ZHANG Liang, HAI Jinke. Calculation of Number of Homomorphisms of a Class of Metacyclic Groups#br#[J].Journal of Jilin University Science Edition, 2018, 56(5): 1045-1048.

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Calculation of Number of Homomorphisms of a Class of Metacyclic Groups#br#

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