Work

Finite 2-groups with exactly three automorphism orbits

Year: 2025

Type: article

Abstract: We give a complete classification of the finite 2-groups 𝐺 for which the automorphism group Aut ⁡ ( G ) \operatorname{Aut}(G) acting naturally on 𝐺 has three orbits. There are two infinite families and one additional group, of order 2 9 2^{9} . All of them are Suzuki 2-groups, and they appear (in a different context) in an earlier classification of Dornhoff.

Source: Journal of Group Theory

DOI: 10.1515/jgth-2024-0051

Authors: Alexander Bors, Stephen P. Glasby

Institutions: Johannes Kepler University of Linz, The University of Western Australia

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: Austrian Science Fund, Australian Research Council