This article is cited in 4 papers

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.

UDC: 512.5

MSC: 20D99

Received March 13, 2018, published May 17, 2018

Language: English

DOI: 10.17377/semi.2018.15.046

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