International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1449-1453
Groups with the same orders of Sylow normalizers as the Mathieu groups
1Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15914, Iran
2Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran
3Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19838, Iran
Received 17 October 2004
Copyright © 2005 Behrooz Khosravi and Behnam Khosravi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
There exist many characterizations for the sporadic simple groups.
In this paper we give two new characterizations for the Mathieu
sporadic groups. Let be a Mathieu group and let be the
greatest prime divisor of . In this paper, we prove that is uniquely determined by and , where . Also we prove that if is a finite group, then
if and only if for every prime , , where and .