For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospectral to Aut(J2) is unsolvable.
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Translated from Algebra i Logika, Vol. 62, No. 1, pp. 71-75, January-February, 2023. Russian DOI: https://doi.org/10.33048/alglog.2023.62.104.
D. V. Lytkina and V. D. Mazurov are supported by Russian Science Foundation, grant No. 23-41-10003.
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Zhurtov, A.K., Lytkina, D.V. & Mazurov, V.D. Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group. Algebra Logic 62, 50–53 (2023). https://doi.org/10.1007/s10469-023-09723-0
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DOI: https://doi.org/10.1007/s10469-023-09723-0