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Classifying primitive solvable permutation groups of rank 5 and 6

  • Anakin Dey , Kolton O’Neal , Duc Van Khanh Tran , Camron Upshur and Yong Yang ORCID logo EMAIL logo
Published/Copyright: April 30, 2024
Journal of Group Theory
From the journal Journal of Group Theory Volume 27 Issue 6

Abstract

Let 𝐺 be a finite solvable permutation group acting faithfully and primitively on a finite set Ω. Let G 0 be the stabilizer of a point 𝛼 in Ω. The rank of 𝐺 is defined as the number of orbits of G 0 in Ω, including the trivial orbit { α } . In this paper, we completely classify the cases where 𝐺 has rank 5 and 6, continuing the previous works on classifying groups of rank 4 or lower.

Funding source: National Science Foundation

Award Identifier / Grant number: DMS-1757233

Award Identifier / Grant number: DMS-2150205

Funding statement: This research was conducted under NSF-REU grant DMS-1757233 and DMS-2150205 by Anakin Dey, Kolton O’Neal, Duc Van Khanh Tran, and Camron Upshur during the Summer of 2023 under the supervision of Prof. Yong Yang.

Acknowledgements

The authors gratefully acknowledge the financial support of NSF and thank Texas State University for providing a great working environment and support. The authors would also like to thank Professors Thomas Keller and Derek Holt for their invaluable help. Finally, we would like to thank the reviewer for their remarks which have improved this manuscript.

  1. Communicated by: Hung Tong-Viet

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Received: 2023-10-11
Revised: 2024-01-22
Published Online: 2024-04-30
Published in Print: 2024-11-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Open mappings of locally compact groups
  3. Groups of profinite type and profinite rigidity
  4. On conjugate separability of nilpotent subgroups
  5. Groups whose proper subgroups of infinite rank have a permutability transitive relation
  6. A generalization of the Brauer–Fowler theorem
  7. On groups with large verbal quotients
  8. Conjugacy class numbers and nilpotent subgroups of finite groups
  9. On the common transversal probability
  10. Classifying primitive solvable permutation groups of rank 5 and 6
  11. Tuple regularity and 𝑘-ultrahomogeneity for finite groups
  12. Skew-morphisms of elementary abelian 𝑝-groups
  13. On algebraic normalisers of maximal tori in simple groups of Lie type
https://doi.org/10.1515/jgth-2023-0205

Articles in the same Issue

  1. Frontmatter
  2. Open mappings of locally compact groups
  3. Groups of profinite type and profinite rigidity
  4. On conjugate separability of nilpotent subgroups
  5. Groups whose proper subgroups of infinite rank have a permutability transitive relation
  6. A generalization of the Brauer–Fowler theorem
  7. On groups with large verbal quotients
  8. Conjugacy class numbers and nilpotent subgroups of finite groups
  9. On the common transversal probability
  10. Classifying primitive solvable permutation groups of rank 5 and 6
  11. Tuple regularity and 𝑘-ultrahomogeneity for finite groups
  12. Skew-morphisms of elementary abelian 𝑝-groups
  13. On algebraic normalisers of maximal tori in simple groups of Lie type
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