A new characterization of some Mathieu groups by the number of Sylow subgroups

Alireza Khalili Asboei; Syyed Sadegh Salehi Amiri; Ali Iranmanesh; Abolfazl Tehranian

doi:10.5269/bspm.v31i1.14818

A new characterization of some Mathieu groups by the number of Sylow subgroups

Alireza Khalili Asboei Azad University Science and Research Branch Department of Mathematics
Syyed Sadegh Salehi Amiri Azad University Science and Research Branch Department of Mathematics
Ali Iranmanesh Tarbiat Modares University Faculty of Mathematical Sciences Department of Mathematics
Abolfazl Tehranian Azad University Science and Research Branch Department of Mathematics

DOI: https://doi.org/10.5269/bspm.v31i1.14818

Resumo

Let G be a finite group with trivial center and n_{p}(G) be the number of Sylow p- subgroup of G. In this paper we prove that if n_{p}(G)=n_{p}(M_{n}), for every prime p in pi (G), where n in {11, 12}, then M_{n}<= G <= Aut(M_{n}).