A new characterization of some families of finite simple groups

  • M. Foroudi Ghasemabadi

    Tarbiat Modares University, Tehran, Iran
  • Ali Iranmanesh

    Tarbiat Modares University, Tehran, Iran
  • M. Ahanjideh

    Tarbiat Modares University, Tehran, Iran

Abstract

Let GG be a finite group. A vanishing element of GG is an element gGg\in G such that χ(g)=0\chi(g)=0 for some irreducible complex character χ\chi of GG. Denote by Vo(G){\rm Vo}(G) the set of the orders of vanishing elements of GG. In this paper, we prove that if GG is a finite group such that Vo(G)=Vo(M){\rm Vo}(G)={\rm Vo}(M) and G=M|G|=|M|, then GMG\cong M, where MM is a sporadic simple group, an alternating group, a projective special linear group L2(p)L_2(p), where pp is an odd prime or a finite simple KnK_{n}-group, where n{3,4}n\in \{3,4\}. These results confirm the conjecture posed in [17] for the simple groups under study.

Cite this article

M. Foroudi Ghasemabadi, Ali Iranmanesh, M. Ahanjideh, A new characterization of some families of finite simple groups. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 57–74

DOI 10.4171/RSMUP/137-3