# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 137, 2017, pp. 57–74**

**DOI: 10.4171/RSMUP/137-3**

Published online: 2017-05-12

A new characterization of some families of finite simple groups

M. Foroudi Ghasemabadi^{[1]}, Ali Iranmanesh

^{[2]}and M. Ahanjideh

^{[3]}(1) Tarbiat Modares University, Tehran, Iran

(2) Tarbiat Modares University, Tehran, Iran

(3) Tarbiat Modares University, Tehran, Iran

Let $G$ be a finite group. A vanishing element of $G$ is an element $g\in G$ such that $\chi(g)=0$ for some irreducible complex character $\chi$ of $G$. Denote by ${\rm Vo}(G)$ the set of the orders of vanishing elements of $G$. In this paper, we prove that if $G$ is a finite group such that ${\rm Vo}(G)={\rm Vo}(M)$ and $|G|=|M|$, then $G\cong M$, where $M$ is a sporadic simple group, an alternating group, a projective special linear group $L_2(p)$, where $p$ is an odd prime or a finite simple $K_{n}$-group, where $n\in \{3,4\}$. These results confirm the conjecture posed in [17] for the simple groups under study.

*Keywords: *Finite simple groups, zeros of characters

Foroudi Ghasemabadi M., Iranmanesh Ali, Ahanjideh M.: A new characterization of some families of finite simple groups. *Rend. Sem. Mat. Univ. Padova* 137 (2017), 57-74. doi: 10.4171/RSMUP/137-3