The Influence of Hughes Type Action

Abstract

We call the action of an automorphism α of a finite group G a Hughes type action if it is described by conditions on the orders of elements of G ⟨ α ⟩ − G. In the present paper we study the structure of finite group G admitting an automorphism α of prime order p so that the orders of elements in G ⟨ α ⟩ − G are not divisible by p ².

Key Words:

• Automorphisms
• Exceptional action
• Nilpotent length
• p-Length
• Splitting

2010 Mathematics Subject Classification:

• 20D10
• 20D15
• 20D45

Notes

Communicated by V. A. Artamonov.