AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (236.5 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Two theorems on direct products of gyrogroups

Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Show Author Information

Abstract

We extend two standard theorems on groups to gyrogroups: the direct product theorem and the cancellation theorem for direct products. Firstly, we prove that under a certain condition a gyrogroup G can be decomposed as the direct product of two subgyrogroups. Secondly, we prove that finite gyrogroups can be cancelled in direct products: if A ≅ B, then A × H ≅ B × K or H × A ≅ K × B implies H ≅ K, where A , B , H , and K are finite gyrogroups.

Keywords

direct product theoremcancellation theoremdecomposition of gyrogroupgyrogrouphomomorphism
CLC number: Primary 20N05; Secondary 20A05, 20E34

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6278-6287
DOI: 10.3934/math.2023317

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Suksumran T. Two theorems on direct products of gyrogroups. AIMS Mathematics, 2023, 8(3): 6278-6287. https://doi.org/10.3934/math.2023317

10

Views

0

Downloads

1

Crossref

1

Web of Science

2

Scopus
Received: 30 October 2022
Revised: 12 December 2022
Accepted: 21 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)