Abstract
Let G be a finite group. An element g ∈ G is called a vanishing element if there exists an irreducible complex character χ of G such that χ(g)= 0. Denote by Vo(G) the set of orders of vanishing elements of G. Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let G be a finite group and M a finite nonabelian simple group such that Vo(G) = Vo(M) and |G| = |M|. Then G ≌ M. We answer in affirmative this conjecture for M = Sz(q), where q = 22n+1 and either q − 1, \(q - \sqrt {2q} + 1\) or q + \(\sqrt {2q} + 1\) is a prime number, and M = F4(q), where q = 2n and either q4 + 1 or q4 − q2 + 1 is a prime number.
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Khatami, M., Babai, A. Recognition of some families of finite simple groups by order and set of orders of vanishing elements. Czech Math J 68, 121–130 (2018). https://doi.org/10.21136/CMJ.2018.0355-16
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DOI: https://doi.org/10.21136/CMJ.2018.0355-16