A New Characterization of Simple K₃-Groups

Abstract

It is a well-known topic to characterize a finite simple group by using two quantities the order of G and π _e (G) in the past 30 years, where π _e (G) denotes the set of orders of elements in G. Recently this topic has been finished by Mazurov et al. Here the authors will try to characterize some finite simple groups by using less quantities and have successfully characterized simple K ₃-groups by using the order of a group and the largest and the second largest element orders, where a K ₃-group is a group of order containing exactly three distinct primes.

Key Words:

• Characterization
• Simple K ₃-group
• The largest element order
• The order of a group
• The second largest element order

2000 Mathematics Subject Classification:

• 20D05
• 20D60

ACKNOWLEDGMENTS

This work is supported by NSF of China (Grant No. 11001226, 11171364), and by Science and Technology Project of Chongqing Education Committee (No. KJ 110609), and by Natural Science Foundation Project of Chongqing (No. CSTS, 2011jjA00020). We thank anonymous reviewers for their thoughtful comments.

Notes

Communicated by V. A. Artamonov.