A New Characterization of A₂₂ by Its Spectrum

Abstract

It is proved that a finite group whose element order set is the same as that of an alternating group A ₂₂ of degree 22 is isomorphic to A ₂₂.

Key Words:

• Alternating groups
• Element orders
• Finite group

2000 Mathematics Subject Classification:

• 20D05
• 20D60

ACKNOWLEDGMENTS

The authors would like to thank the referee with deep gratitude for pointing out some mistakes in a previous version of the article, especially his/her valuable suggestions on revising the article, which make the proof of theorem read smoothly and more technically.

Notes

Communicated by A. Olshanskii.