Finite 2-groups with exactly three automorphism orbits

Alexander Bors; Stephen P. Glasby

doi:10.1515/jgth-2024-0051

Finite 2-groups with exactly three automorphism orbits

Alexander Bors, Stephen P. Glasby

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article › peer-review

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 a different context) in an earlier classification of Dornhoff.

Original language	English
Number of pages	25
Journal	Journal of Group Theory
DOIs	https://doi.org/10.1515/jgth-2024-0051
Publication status	E-pub ahead of print - 3 Apr 2025

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10.1515/jgth-2024-0051Licence: CC BY

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title = "Finite 2-groups with exactly three automorphism orbits",

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 a different context) in an earlier classification of Dornhoff.",

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AB - 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 a different context) in an earlier classification of Dornhoff.

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Finite 2-groups with exactly three automorphism orbits

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Complexity of group algorithms and statistical fingerprints of groups

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Finite 2-groups with exactly three automorphism orbits

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Complexity of group algorithms and statistical fingerprints of groups

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