一类非交换内循环群到有限群的同态个数

Journal of Jilin University Science Edition ›› 2020, Vol. 58 ›› Issue (6): 1299-1302.

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Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups

ZHANG Liang

College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China

Online:2020-11-18 Published:2020-11-26

Abstract

Abstract: Firstly, by using group theory and congruence theory, the author calculated the number of endomorphisms and automorphisms between a class of non commutative inner cyclic groups, and gave the quantity relation of the number of homomorphisms from such inner cyclic groups to finite groups. Secondly, the author verified that the conjectures of Asai and Yoshida were true for the above cases.

Key words: inner cyclic groups, homomorphism, endomorphism, automorphism

CLC Number:

O152.1

ZHANG Liang. Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups[J].Journal of Jilin University Science Edition, 2020, 58(6): 1299-1302.

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Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups

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