关于一类有限 p-群的因子分解数

doi:10.13371/j.cnki.chin.q.j.m.2022.02.003

数学季刊 ›› 2022, Vol. 37 ›› Issue (2): 132-141.doi: 10.13371/j.cnki.chin.q.j.m.2022.02.003

关于一类有限 p-群的因子分解数

Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

收稿日期:2022-01-03 出版日期:2022-06-30 发布日期:2022-06-30
通讯作者: WANG Yu-lei (1979-), male, native of Nanyang, Henan, associate professor of Henan University of Technology, engages in algebra; E-mail:yulwang@163.com
作者简介:WANG Yu-lei (1979-), male, native of Nanyang, Henan, associate professor of Henan University of Technology, engages in algebra; BAI Xue (1998-), female, native of Zhoukou, Henan, master student of Henan University of Technology, engages in algebra; ZHANG Yuan-feng (1995-), male, native of Sanmenxia, Henan, master student of Henan University of Technology, engages in algebra.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 11601121, 12171142).

On the Factorization Numbers of a Class of Finit p-Groups

Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

Received:2022-01-03 Online:2022-06-30 Published:2022-06-30
Contact: WANG Yu-lei (1979-), male, native of Nanyang, Henan, associate professor of Henan University of Technology, engages in algebra; E-mail:yulwang@163.com
About author:WANG Yu-lei (1979-), male, native of Nanyang, Henan, associate professor of Henan University of Technology, engages in algebra; BAI Xue (1998-), female, native of Zhoukou, Henan, master student of Henan University of Technology, engages in algebra; ZHANG Yuan-feng (1995-), male, native of Sanmenxia, Henan, master student of Henan University of Technology, engages in algebra.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11601121, 12171142).

摘要/Abstract

摘要： Let G be a group and A and B be subgroups of G. If G = AB, then G is said
to be factorized by A and B. Let p be a prime number. The factorization numbers of
a 2-generators abelian p-group and a modular p-group have been determined. Further,
suppose that G is a finite p-group as follows G = <a,b|_apⁿ= _bp^m=1 , a^b =_apⁿ⁻¹⁺¹>, where n≥ 2, m≥ 1. In this paper, the factorization number of G is computed completely, which
is a generalization of the result of Saeedi and Farrokhi.

关键词: Finite p-group, Factorization number, Subgroup commutativity degree

Abstract: Let G be a group and A and B be subgroups of G. If G = AB, then G is said
to be factorized by A and B. Let p be a prime number. The factorization numbers of
a 2-generators abelian p-group and a modular p-group have been determined. Further,
suppose that G is a finite p-group as follows G = <a,b|_apⁿ= _bp^m=1 , a^b =_apⁿ⁻¹⁺¹>, where n≥ 2, m≥ 1. In this paper, the factorization number of G is computed completely, which
is a generalization of the result of Saeedi and Farrokhi.

Key words: Finite p-group, Factorization number, Subgroup commutativity degree

中图分类号:

O152.1

王玉雷, 白雪, 张元峰. 关于一类有限 p-群的因子分解数[J]. 数学季刊, 2022, 37(2): 132-141.

WANG Yu-lei, BAI Xue, ZHANG Yuan-feng. On the Factorization Numbers of a Class of Finit p-Groups[J]. Chinese Quarterly Journal of Mathematics, 2022, 37(2): 132-141.

关于一类有限 p-群的因子分解数

On the Factorization Numbers of a Class of Finit p-Groups

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