Abstract
Let G be a finite group. A vanishing element of G is g ∈ G such that χ(g) = 0 for some χ ∈ Irr(G) of the set of irreducible complex characters of G. Denote by Vo(G) the set of the orders of vanishing elements of G. A finite group G is called a VCP-group if every element in Vo(G) is of prime power order. The main purpose of this paper is to investigate a new characterization related to Vo(G) for all finite nonabelian simple VCP-groups. We prove that if G is a finite group and M is a finite nonabelian simple VCP-group such that Vo(G) = Vo(M) and |G| = |M|, then G ≅ M.
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Original Russian Text Copyright © 2015 Ghasemabadi M.F., Iranmanesh A., and Mavadatpour F.
The first two authors were supported in part by the Iran National Science Foundation (INSF) (Grant 91058621).
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Tehran. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 1, pp. 94–99, January–February, 2015.
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Ghasemabadi, M.F., Iranmanesh, A. & Mavadatpour, F. A new characterization of some finite simple groups. Sib Math J 56, 78–82 (2015). https://doi.org/10.1134/S0037446615010073
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DOI: https://doi.org/10.1134/S0037446615010073