Geodesic
On Thompson's conjecture for finite simple exceptional groups of Lie type
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 100-107

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Let $G$ be a finite group and $N(G)$ be its set of conjugacy class sizes. In the present paper it is proved $G\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group of exceptional Lie type. 
@article{ZNSL_2019_478_a4,
     author = {I. B. Gorshkov and I. B. Kaygorodov and A. V. Kukharev and A. A. Shlepkin},
     title = {On {Thompson's} conjecture for finite simple exceptional groups of {Lie} type},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {100--107},
     publisher = {mathdoc},
     volume = {478},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a4/}
}
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%J Zapiski Nauchnykh Seminarov POMI
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I. B. Gorshkov; I. B. Kaygorodov; A. V. Kukharev; A. A. Shlepkin. On Thompson's conjecture for finite simple exceptional groups of Lie type. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 100-107. http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a4/