Geodesic
On recognition of~$A_6\times A_6$ by the set of conjugacy class sizes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 762-767

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For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. Recently the following question has been asked: Is it true that for each nonabelian finite simple group $S$ and each $n\in\mathbb{N}$, if the set of class sizes of a finite group $G$ with trivial center is the same as the set of class sizes of the direct power $S^n$, then $G\simeq S^n$? In this paper we approach an answer to this question by proving that $A_6\times A_6$ is uniquely determined by $N(A_6\times A_6)$ among finite groups with trivial center.
Keywords: finite groups, class sizes.
Mots-clés : conjugacy classes 
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     author = {V. Panshin},
     title = {On recognition of~$A_6\times A_6$ by the set of conjugacy class sizes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {762--767},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a4/}
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V. Panshin. On recognition of~$A_6\times A_6$ by the set of conjugacy class sizes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 762-767. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a4/