Factorization Numbers of a Class of Finite p-groups

WANG Yu-lei, ZHANG Yuan-feng, GUO Peng

doi:10.13371/j.cnki.chin.q.j.m.2018.04.010

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 4: 434 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.04.010

Factorization Numbers of a Class of Finite p-groups

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Department of Mathematics, Henan University of Technology

WANG Yu-lei(1979-), male, native of Nanyang, Henan, associate professor of Henan University of Technology, Ph.D., engager in algebra.

Accepted date: 2016-04-15

Online published: 2020-10-07

Supported by

Supported by National Natural Science Foundation of China(11601121)； Henan Provincial Natural Science Foundation of China(162300410066)；

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Abstract

Let p be a prime number and f₂（G） be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G =< a, b |_apⁿ= _bp^m= 1, a^b= _ap^n-1+1>, where n > m ≥ 1. In this article, the factorization number f₂（G） of G is computed, improving the results of Saeedi and Farrokhi in [5].

Key words： finite p-group; factorization number; subgroup commutativity degree

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WANG Yu-lei, ZHANG Yuan-feng, GUO Peng . Factorization Numbers of a Class of Finite p-groups[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(4) : 434 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.04.010

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