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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 570–584 (Mi semr937)

Mathematical logic, algebra and number theory

On finite groups isospectral to the simple groups $S_4(q)$

Yuri V. Lytkin

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: The spectrum of a finite group is the set of its element orders. A finite group $G$ is critical with respect to a subset $\omega$ of the natural numbers if $\omega$ coincides with the spectrum of $G$ and does not coincide with the spectra of proper sections of $G$. We study the structure of groups with spectra equal to the spectra of the simple symplectic groups $PSp(4,q)$, where $q > 3$ and $q \neq 5$. In particular, we describe the structure of the groups critical with respect to the spectra of $PSp(4,q)$.

Keywords: finite group, spectrum, critical group, nonabelian simple group.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-31-00147_ìîë_à The reported study was funded by RFBR according to the research project No. 16–31–00147.

DOI: https://doi.org/10.17377/semi.2018.15.046

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UDC: 512.5
MSC: 20D99
Received March 13, 2018, published May 17, 2018
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Citation: Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. Èlektron. Mat. Izv., 15 (2018), 570–584

Citation in format AMSBIB
\Bibitem{Lyt18} \by Yuri~V.~Lytkin \paper On finite groups isospectral to the simple groups~$S_4(q)$ \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 570--584 \mathnet{http://mi.mathnet.ru/semr937} \crossref{https://doi.org/10.17377/semi.2018.15.046} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200046} `