Finite 2-groups with exactly three automorphism orbits

2020/11/25 by Bors, Alexander, Glasby, Stephen P.
#20B10 #20D45. Secondary: 12E20 #FOS: Mathematics #Group Theory (math.GR) #Primary: 20D15

paper · doi:10.48550/arxiv.2011.13016

Abstract

We give a complete classification of the finite 2-groups G for which the automorphism group Aut(G) acting naturally on G has three orbits. There are two infinite families and one additional group, of order 2⁹. All of them are Suzuki 2-groups, and they appear in an earlier classification of Dornhoff.

Related

• Classifying finite groups G with three Aut(G)-orbits
• The finite groups with three automorphism orbits
• Finite groups with only small automorphism orbits
• Automorphism groups of 2-groups of coclass at most 3
• Finite 2-groups of Class 2 with Specific Automorphism Group