International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 797-799

A lower bound on the number of finite simple groups

Michael E. Mays

Department of Mathematics, West Virginia University, Morgantown 26506, West Virginia, USA

Received 5 March 1980

Copyright © 1980 Michael E. Mays. 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.


Let S(n)=|{m<n: there is a (non-cyclic) simple group of order m}|. Investigation of known families of simple groups provides the lower bound S(n)n1/4/logn.