Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 121–130 | Cite as

Recognition of some families of finite simple groups by order and set of orders of vanishing elements

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Abstract

Let G be a finite group. An element gG 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 GM. 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 = 2 n and either q4 + 1 or q4q2 + 1 is a prime number.

Keywords

finite simple groups vanishing element vanishing prime graph 

MSC 2010

20C15 20D05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.Department of MathematicsUniversity of QomQomIran

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