Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 121–130

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

Article

## 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

20C15 20D05

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