Abstract
We study the problem concerning the influence of the index of maximal subgroup or the degree of primitive permutation representation of the finite simple groups on the structure of a group. Let G be a finite group and s be the index of maximal subgroup of the Monster M. In this paper, we prove that there exists an epimorphism from G to M or A s if G has the primitive permutation representation of degree s, and as a consequence we prove that the Monster is determined by every s.
Key Words:
Acknowledgments
Li was supported by the NSF of Jiangsu Province and Jiangsu Province Colleges and Universities (Grant No. BK2001133, 03KJB110112).
Notes
#Communicated by A. Olshanskii.