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A note on 𝑑-maximal 𝑝-groups

  • Messab Aiech , Hanifa Zekraoui and Yassine Guerboussa EMAIL logo
Published/Copyright: July 4, 2023
Journal of Group Theory
From the journal Journal of Group Theory Volume 27 Issue 1

Abstract

A finite 𝑝-group 𝐺 is said to be 𝑑-maximal if d ⁒ ( H ) < d ⁒ ( G ) for every subgroup H < G , where d ⁒ ( G ) denotes the minimal number of generators of 𝐺. A similar definition can be formulated when 𝐺 is acted on by some group 𝐴. In this paper, we extend earlier results of Kahn and Laffey to this more general setting and we answer a question of Berkovich on minimal non-metacyclic 𝑝-groups.

Acknowledgements

We would like to thank the referees for their invaluable comments and suggestions which have considerably improved the presentation of this paper. We are also grateful to Professor Bruno Kahn for several enlightening comments and for providing us with some of his early manuscripts on the subject. The first author would like to thank Professor B. Eick for her hospitality during his visit to UniversitΓ€t Braunschweig and for the invaluable things he learned from her.

  1. Communicated by: Benjamin Klopsch

References

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Received: 2022-04-13
Revised: 2023-05-30
Published Online: 2023-07-04
Published in Print: 2024-01-01

Β© 2023 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Elementary amenable groups of cohomological dimension 3
  3. The nilpotent genus of finitely generated residually nilpotent groups
  4. Quantifying lawlessness in finitely generated groups
  5. On multidimensional Schur rings of finite groups
  6. A classification of the prime graphs of pseudo-solvable groups
  7. On generations by conjugate elements in almost simple groups with socle 2𝐹4(π‘ž2)β€²
  8. A characterization of the simple Ree groups 2𝐹4(π‘ž2) by their character codegrees
  9. A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters
  10. Class-two quotients of finite permutation groups
  11. A note on 𝑑-maximal 𝑝-groups
https://doi.org/10.1515/jgth-2022-0071

Articles in the same Issue

  1. Frontmatter
  2. Elementary amenable groups of cohomological dimension 3
  3. The nilpotent genus of finitely generated residually nilpotent groups
  4. Quantifying lawlessness in finitely generated groups
  5. On multidimensional Schur rings of finite groups
  6. A classification of the prime graphs of pseudo-solvable groups
  7. On generations by conjugate elements in almost simple groups with socle 2𝐹4(π‘ž2)β€²
  8. A characterization of the simple Ree groups 2𝐹4(π‘ž2) by their character codegrees
  9. A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters
  10. Class-two quotients of finite permutation groups
  11. A note on 𝑑-maximal 𝑝-groups
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