International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1449-1453
doi:10.1155/IJMMS.2005.1449
Groups with the same orders of Sylow normalizers as the Mathieu groups.
Behrooz Khosravi1
and Behnam Khosravi2
1Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15914, Iran
2Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19838, Iran
Abstract
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).