Lengths of conjugacy classes of π-elements and primary elements in finite groups

Abstract

In this paper, we study how certain arithmetical conditions on the lengths of conjugacy classes of primary elements and π-elements of a finite group G influence the structure of G, some new results are obtained and several well-known results in the literature are developed. In particular, the structure of a kind of outer p-supersolvable groups is described, some new conditions implying π-supersolvability are found, and the upper bound for the order of Sylow subgroups is discussed.

Keywords:

• Conjugacy class lengths
• P-groups
• π-nilpotent groups
• π-supersolvable groups

2020 Mathematics Subject Classification:

• 20D15
• 20E34
• 20F18

4 Acknowledgments

The authors is grateful to the referee for careful reading of the manuscript and for many helpful suggestions and corrections. As a result, the exposition of our paper has been improved significantly.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant nos. 12261022, 11871360).