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Mathematical logic, algebra and number theory

On finite groups isospectral to the simple group $S_4(3)$

Yuri V. Lytkin

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

Abstract: The spectrum of a finite group is the set of its element orders. A finite group $G$ is called critical with respect to a subset $\omega$ of 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 finite groups with the same spectrum as the simple symplectic group $PSp(4, 3)$. In particular, we describe groups critical with respect to the spectrum of $PSp(4, 3)$.

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

UDC: 512.5

MSC: 20D99

Received March 3, 2019, published October 31, 2019

Language: English

DOI: 10.33048/semi.2019.16.107

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