On Finite Groups with Few Automorphism Orbits. Issue 7 (2nd July 2016)

• Record Type: Journal Article
• Authors: Bastos, Raimundo; Dantas, Alex Carrazedo
• Is Part Of: Communications in algebra. Volume 44:Issue 7(2016)
• Page Start: 2953
• Page End: 2958
• Publication Date: 2016-07-02
• Subjects: Automorphism groups -- Finite groups; 20D05 -- 20D45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1065856
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Denote by ω( G ) the number of orbits of the action of Aut ( G ) on the finite group G . We prove that if G is a finite nonsolvable group in which ω( G ) ≤5, then G is isomorphic to one of the groups A 5, A 6, PSL (2, 7), or PSL (2, 8). We also consider the case when ω( G ) = 6 and show that, if G is a nonsolvable finite group with ω( G ) = 6, then either G ≈ PSL (3, 4) or there exists a characteristic elementary abelian 2-subgroup N of G such that G / N ≈ A 5 .