一类内交换p-群与四元数群之间的同态个数

doi:10.6040/j.issn.1671-9352.0.2021.411

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 45-49.doi: 10.6040/j.issn.1671-9352.0.2021.411

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一类内交换p-群与四元数群之间的同态个数

廖青清,郭继东^*,张良

伊犁师范大学数学与统计学院, 新疆伊宁 835000

发布日期:2022-01-07
作者简介:廖青清(1998— ),女,硕士研究生,研究方向为群论. E-mail:1767916013@qq.com*通信作者简介:郭继东(1965— ),男,教授,研究方向为群论. E-mail:guojd662@163.com
基金资助:
新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2020I018)

Number of homomorphisms between intra-commutative p-groups and quaternion groups

LIAO Qing-qing, GUO Ji-dong^*, ZHANG Liang

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

Published:2022-01-07

摘要/Abstract

摘要： 根据内交换p-群和四元数群的结构特征以及元素的性质,计算了一类内交换p-群和四元数群之间的同态个数,并验证了T.Asai和T.Yoshida猜想对此类群成立。

关键词: 内交换p-群, 四元数群, 群同态

Abstract: Based on the group structure and element properties of intra-commutative p-groups and quaternion groups, the number of homomorphisms from a class of intra-commutative p-groups into quaternion groups is calculated. As an application, the conjecture of T.Asai and T.Yoshida is proved to be valid for such groups.

Key words: intra-commutative p-groups, quaternion groups, group homomorphism

中图分类号:

O152.6

廖青清,郭继东,张良. 一类内交换p-群与四元数群之间的同态个数[J]. 《山东大学学报(理学版)》, 2022, 57(2): 45-49.

LIAO Qing-qing, GUO Ji-dong, ZHANG Liang. Number of homomorphisms between intra-commutative p-groups and quaternion groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 45-49.

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一类内交换p-群与四元数群之间的同态个数

Number of homomorphisms between intra-commutative p-groups and quaternion groups

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