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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 1698–1704
DOI: https://doi.org/10.33048/semi.2021.18.129 (Mi semr1470) 		 
Mathematical logic, algebra and number theory

The sum of orders of elements in nonabelian groups of odd order

A. A. Buturlakina, A. F. Tereshchenkob

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Siberian State University of Telecommunications and Informatics, 86, Kirov str., Novosibirsk, 630102, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.129
Abstract: Denote by $\psi(G)$ the sum of the orders of the elements of a finite group $G$. We obtain an exact upper bound for $\psi(G)$ on the set of nonabelian groups of given odd order $n$ in terms of the minimal prime divisor of $n$. We also describe the finite groups on which this bound is achieved.
Keywords: orders of elements, solvable groups.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-00007
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0001
The work is supported by RFBR and BRFBR (grant 20-51-00007), and was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0001).
Received November 1, 2021, published December 28, 2021
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D60
Language: English
Citation: A. A. Buturlakin, A. F. Tereshchenko, “The sum of orders of elements in nonabelian groups of odd order”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1698–1704
Citation in format AMSBIB
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\by A.~A.~Buturlakin, A.~F.~Tereshchenko
\paper The sum of orders of elements in nonabelian groups of odd order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 1698--1704
\mathnet{http://mi.mathnet.ru/semr1470}
\crossref{https://doi.org/10.33048/semi.2021.18.129}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000747257800002}
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