M. A. Zvezdina, “Spectra of automorphic extensions of finite simple exceptional groups of Lie type”, Algebra Logika, 2016, Volume 55, Number 5,Pages <nobr>540

This article is cited in 8 papers

Spectra of automorphic extensions of finite simple exceptional groups of Lie type

M. A. Zvezdina^ab

^a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: The spectrum $\omega(G)$ of a finite group $G$ is the set of orders of elements of $G$. Let $S$ be a simple exceptional group of type $E_6$ or $E_7$. We describe all finite groups $G$ such that $S\le G\le\operatorname{Aut}S$ and $\omega(G)=\omega(S)$. Along with the previously obtained results, this provides a description of all finite groups $G$ such that $\omega(G)=\omega(S)$ and completes the study of the recognition-by-spectrum problem for all simple exceptional groups of Lie type.

Keywords: automorphic extension, exceptional group, finite simple group, order of element, recognizability by spectrum.

UDC: 512.542

Received: 11.12.2015

DOI: 10.17377/alglog.2016.55.502