一类有限2群与二面体群之间的同态个数

doi:10.6040/j.issn.1671-9352.0.2022.209

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 7-13.doi: 10.6040/j.issn.1671-9352.0.2022.209

一类有限2群与二面体群之间的同态个数

张薇^1,2,赖吉娜^1,2,郭继东^1,2*,张良^1,2

1.伊犁师范大学数学与统计学院, 新疆伊宁 835000;2.伊犁师范大学应用数学研究所, 新疆伊宁 835000

发布日期:2023-03-02
作者简介:张薇(1998— ),女,硕士研究生,研究方向为群论. E-mail:zw108853@163.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:
新疆维吾尔自治区自然科学基金项目(2022D01C334);2022年度伊梨师范大学高级别培育项目(YSPY2022012)

The number of homomorphisms between a class of finite 2-groups and dihedral groups

ZHANG Wei^1,2, LAI Ji-na^1,2, GUO Ji-dong^1,2*, ZHANG Liang^1,2

1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
2. Institute of applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China

Published:2023-03-02

摘要/Abstract

摘要： 根据G2和二面体群的结构特征以及元素的性质,计算G2和二面体群之间的同态个数。作为应用,验证这两个群之间的同态个数满足T.Asai和T.Yoshida 的猜想。

关键词: 有限2群, 二面体群, 群同态

Abstract: Based on the group structure and element properties of G₂ and dihedral groups, the number of homomorphisms between G₂ and dihedral groups is calculated. As an application, it verifies that T.Asai and T.Yoshidas conjecture is satisfied such groups.

Key words: finite 2-groups, dihedral groups, group homomorphism

中图分类号:

O152.6

张薇,赖吉娜,郭继东,张良. 一类有限2群与二面体群之间的同态个数[J]. 《山东大学学报(理学版)》, 2023, 58(3): 7-13.

ZHANG Wei, LAI Ji-na, GUO Ji-dong, ZHANG Liang. The number of homomorphisms between a class of finite 2-groups and dihedral groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(3): 7-13.

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一类有限2群与二面体群之间的同态个数

The number of homomorphisms between a class of finite 2-groups and dihedral groups

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