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

WANG Yu-lei, BAI Xue, ZHANG Yuan-feng

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

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 2: 132 - 141

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.02.003

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

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

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.

Received date: 2022-01-03

Online published: 2022-06-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11601121, 12171142).

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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

Cite this article

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

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