Groups with the same orders of Sylow normalizers as the Mathieu groups

oleh: Behrooz Khosravi, Behnam Khosravi

Format: Article
Diterbitkan: Wiley 2005-01-01

Deskripsi

There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the greatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where P∈Sylp(M). Also we prove that if G is a finite group, then G≅M if and only if for every prime q, |NM(Q)|=|NG(Q′)|, where Q∈Sylq(M) and Q′∈Sylq(G).