The order of the product of two elements

Xianhua Li (), Donglin Lei and Yaxin Gao
Additional contact information
Xianhua Li: Soochow University
Donglin Lei: Soochow University
Yaxin Gao: Soochow University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 372-374

Abstract: Abstract We prove that in a finite group G, $$|ab|=|a||b|$$ | a b | = | a | | b | if and only if $$ab=ba$$ a b = b a for all elements a, b of G whose orders are factor of the m-th power of different primes, where m is a given integer.

Keywords: Finite group; Nilpotent group; Elements of co-prime order; Product; 20B05; 20D15 (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s13226-021-00007-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00007-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-021-00007-w

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().