On Permutation Groups of Degree a Product of Two Prime-Powers

Abstract

We determine finite simple groups which have a subgroup of index with exactly two distinct prime divisors. Then from this we derive a classification of primitive permutation groups of degree a product of two prime-powers.

Key Words:

• Finite simple group
• Permutation groups
• Primitive

2010 Mathematics Subject Classification:

• 20B15

ACKNOWLEDGMENT

The author is very grateful to the referee who read the manuscript carefully and provided several comments.

Notes

Communicated by A. Turull.