Geodesic
Spectra of automorphic extensions of finite simple exceptional groups of Lie type
Algebra i logika, Tome 55 (2016) no. 5, pp. 540-557

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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, finite simple group, order of element, recognizability by spectrum.
Mots-clés : exceptional group 
@article{AL_2016_55_5_a1,
     author = {M. A. Zvezdina},
     title = {Spectra of automorphic extensions of finite simple exceptional groups of {Lie} type},
     journal = {Algebra i logika},
     pages = {540--557},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_5_a1/}
}
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M. A. Zvezdina. Spectra of automorphic extensions of finite simple exceptional groups of Lie type. Algebra i logika, Tome 55 (2016) no. 5, pp. 540-557. http://geodesic.mathdoc.fr/item/AL_2016_55_5_a1/