A criterion for the existence of a solvable π-Hall subgroup in a finite group

Abstract

Let G be a finite group and let π be a set of primes. We prove that G has a solvable π-Hall subgroup if and only if G has a {p, q}-Hall subgroup for every pair p, q ∈ π.

Keywords:

• Finite group
• solvable group
• Hall subgroup

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D20
• 20F16

Acknowledgements

We want to thank D.O. Revin for discussions on the subject of the paper. The paper was funded by RFBR (project 18-31-20011).