Let G be a finite group. We say that an element g of G is a vanishing element if there exists an irreducible complex character 𝜒 of G such that (g) = 0. Ghasemabadi, Iranmanesh, and Mavadatpour (2015) made the following conjecture: Let G be a finite group and let M be a finite non-Abelian simple group such that Vo(G) = Vo(M) and |G| = |M|. Then G ≅ M. We give an affirmative answer to this conjecture for M = 2Dr+1(2), where r = 2n − 1 ≥ 3 and either 2r + 1 or 2r+1 + 1 is a prime number, and M = 2Dr(3), where r = 2n + 1 ≥ 5 and either (3r−1 + 1)/2 or (3r + 1)/4 is prime.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 11, pp. 1443–1450, November, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i11.1069.
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Askary, S. Characterization of Some Finite Simple Groups by the Set of Orders of Vanishing Elements and Order. Ukr Math J 73, 1663–1673 (2022). https://doi.org/10.1007/s11253-022-02022-4
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DOI: https://doi.org/10.1007/s11253-022-02022-4