Sum of Element Orders of Maximal Subgroups of the Symmetric Group

Abstract

For a finite group G, let ψ(G) denote the sum of element orders of G. The aim of this article is to show that ψ(H) < ψ(A _n ) for every proper subgroup H of the symmetric group of degree n, which is different from the alternating group A _n .

Key Words:

• Element orders
• Maximal subgroups
• Symmetric group

2000 Mathematics Subject Classification:

• 20D60

ACKNOWLEDGMENTS

The authors are very grateful to the referee for his/her valuable comments. Also the authors are grateful to Professor Alireza Abdollahi for his reading and useful comments.

Notes

Communicated by A. Turull.