Recognition by order and set of orders of vanishing elements of C_n (2^α), for some n and α

چکیده مقاله

We say that an element g in a finite group G is a vanishing element of G if there exists an irreducible character χ ∈ Irr(G) such that χ(g) = 0. The set of orders of vanishing elements of G is denoted by Vo(G). In [5], the authors put forward the following conjecture: If G is a finite group and M is a finite nonabelian simple group such that Vo(G) = Vo(M) and |G| = |M|, then G= M. In this paper we answer positive to this conjecture for a family of classical simple groups C_n(q), where n = 2^m ≥ 2, q = 2^α and qⁿ + 1 is a prime. © 2018, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved.