On quantitative structure of small Ree groups

ABSTRACT

The main aim of this article is to study quantitative structure of small Ree Groups ²G₂(q). Here, we prove that small Ree groups are uniquely determined by their orders and the set of the number of elements of the same order.

KEYWORDS:

• Element order
• simple group
• small Ree group
• Thompson’s problem

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20D60
• Secondary: 20D06

Acknowledgments

The authors are grateful to the anonymous referees and the editor for careful reading of the manuscript and for corrections and suggestions.