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Minimal degrees for faithful permutation representations of groups of order 𝑝5 where 𝑝 is an odd prime

  • Sunil Kumar Prajapati and Ayush Udeep EMAIL logo
Published/Copyright: May 22, 2025
Journal of Group Theory
From the journal Journal of Group Theory Volume 28 Issue 6

Abstract

In a 2018 paper, Behravesh and Delfani computed the minimal degree of a faithful permutation representation for groups of order p 5 , where 𝑝 is an odd prime. However, their results are incorrect and incomplete: some groups are not considered, some minimal degrees are incorrectly determined, and the reported list of degrees is incomplete. We determine the minimal degree of a faithful permutation representation for each group of order p 5 , where 𝑝 is an odd prime. We also record how to obtain such a representation.

Funding source: Science and Engineering Research Board

Award Identifier / Grant number: MTR/2019/000118

Funding statement: Sunil K. Prajapati acknowledges the Science and Engineering Research Board, Government of India, for financial support through grant MTR/2019/000118.

Acknowledgements

Ayush Udeep thanks the Indian Institute of Science Education and Research Mohali for his Postdoctoral Fellowship. We thank M. F. Newman who alerted us to the errors in [2], and E. A. O’Brien for carefully reading the many versions of this paper and elaborate discussions on the content. The authors acknowledge the University of Auckland for providing remote access to their computational facilities.

  1. Communicated by: Bettina Eick

References

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Received: 2024-11-01
Revised: 2025-04-12
Published Online: 2025-05-22
Published in Print: 2025-11-01

Β© 2025 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Bounding the degree of generic sharp transitivity
  3. Structure of an exotic 2-local subgroup in 𝐸7(π‘ž)
  4. Set-stabilizers in solvable permutation groups
  5. Regular saturated formations of finite soluble groups
  6. On the 𝑝-length and π”˜-class of a 𝑝-solvable finite group
  7. Finite 2-groups with exactly three automorphism orbits
  8. Finite class 2 nilpotent and Heisenberg groups
  9. Minimal degrees for faithful permutation representations of groups of order 𝑝5 where 𝑝 is an odd prime
  10. 𝜏-Tilting finiteness of group algebras of semidirect products of abelian 𝑝-groups and abelian 𝑝′-groups
  11. On the Grossman representations of the automorphism groups of free groups
  12. Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
  13. The proper geometric dimension of the mapping class group of an orientable surface with punctures
  14. A note on complex hyperbolic lattices and strict hyperbolization
https://doi.org/10.1515/jgth-2024-0199

Articles in the same Issue

  1. Frontmatter
  2. Bounding the degree of generic sharp transitivity
  3. Structure of an exotic 2-local subgroup in 𝐸7(π‘ž)
  4. Set-stabilizers in solvable permutation groups
  5. Regular saturated formations of finite soluble groups
  6. On the 𝑝-length and π”˜-class of a 𝑝-solvable finite group
  7. Finite 2-groups with exactly three automorphism orbits
  8. Finite class 2 nilpotent and Heisenberg groups
  9. Minimal degrees for faithful permutation representations of groups of order 𝑝5 where 𝑝 is an odd prime
  10. 𝜏-Tilting finiteness of group algebras of semidirect products of abelian 𝑝-groups and abelian 𝑝′-groups
  11. On the Grossman representations of the automorphism groups of free groups
  12. Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
  13. The proper geometric dimension of the mapping class group of an orientable surface with punctures
  14. A note on complex hyperbolic lattices and strict hyperbolization
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