A note on 𝑑-maximal 𝑝-groups
-
Messab Aiech
Abstract
A finite 𝑝-group 𝐺 is said to be 𝑑-maximal if
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 Universität Braunschweig and for the invaluable things he learned from her.
-
Communicated by: Benjamin Klopsch
References
[1] Y. Berkovich, Groups of Prime Power Order. Vol. 1, De Gruyter Exp. Math. 46, Walter de Gruyter, Berlin, 2008. 10.1515/9783110208221Suche in Google Scholar
[2] Y. Berkovich and Z. Janko, Groups of Prime Power Order. Vol. 3, De Gruyter Exp. Math. 56, Walter de Gruyter, Berlin, 2011. Suche in Google Scholar
[3] N. Blackburn, Generalizations of certain elementary theorems on 𝑝-groups, Proc. London Math. Soc. (3) 11 (1961), 1–22. 10.1112/plms/s3-11.1.1Suche in Google Scholar
[4] J. D. Dixon, M. P. F. du Sautoy, A. Mann and D. Segal, Analytic pro-𝑝 Groups, 2nd ed., Cambridge Stud. Adv. Math. 61, Cambridge University, Cambridge, 1999. 10.1017/CBO9780511470882Suche in Google Scholar
[5] J. González-Sánchez and B. Klopsch, On 𝑤-maximal groups, J. Algebra 328 (2011), 155–166. 10.1016/j.jalgebra.2010.07.045Suche in Google Scholar
[6]
Z. Janko,
Finite 2-groups with exactly four cyclic subgroups of order
[7] B. Kahn, The total Stiefel-Whitney class of a regular representation, J. Algebra 144 (1991), no. 1, 214–247. 10.1016/0021-8693(91)90136-VSuche in Google Scholar
[8] B. Kahn, A characterisation of powerfully embedded normal subgroups of a 𝑝-group, J. Algebra 188 (1997), no. 2, 401–408. 10.1006/jabr.1996.6846Suche in Google Scholar
[9] T. J. Laffey, The minimum number of generators of a finite 𝑝-group, Bull. Lond. Math. Soc. 5 (1973), 288–290. 10.1112/blms/5.3.288Suche in Google Scholar
[10] A. Lubotzky and A. Mann, Powerful 𝑝-groups. I. Finite groups, J. Algebra 105 (1987), no. 2, 484–505. 10.1016/0021-8693(87)90211-0Suche in Google Scholar
[11] A. Mann, Some questions about 𝑝-groups, J. Aust. Math. Soc. Ser. A 67 (1999), no. 3, 356–379. 10.1017/S1446788700002068Suche in Google Scholar
[12] P. A. Minh, 𝑑-maximal 𝑝-groups and Stiefel–Whitney classes of a regular representation, J. Algebra 179 (1996), no. 2, 483–500. 10.1006/jabr.1996.0021Suche in Google Scholar
[13] P. A. Minh, On a conjecture of Kahn for the Stiefel–Whitney classes of the regular representation, J. Algebra 188 (1997), no. 2, 590–609. 10.1006/jabr.1996.6817Suche in Google Scholar
[14] J. G. Thompson, A replacement theorem for 𝑝-groups and a conjecture, J. Algebra 13 (1969), 149–151. 10.1016/0021-8693(69)90068-4Suche in Google Scholar
[15] The GAP Group, GAP - Groups, algorithms, and programming, version 4.4.12, www.gap-system.org, 2008. Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Elementary amenable groups of cohomological dimension 3
- The nilpotent genus of finitely generated residually nilpotent groups
- Quantifying lawlessness in finitely generated groups
- On multidimensional Schur rings of finite groups
- A classification of the prime graphs of pseudo-solvable groups
- On generations by conjugate elements in almost simple groups with socle 2𝐹4(𝑞2)′
- A characterization of the simple Ree groups 2𝐹4(𝑞2) by their character codegrees
- A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters
- Class-two quotients of finite permutation groups
- A note on 𝑑-maximal 𝑝-groups
Artikel in diesem Heft
- Frontmatter
- Elementary amenable groups of cohomological dimension 3
- The nilpotent genus of finitely generated residually nilpotent groups
- Quantifying lawlessness in finitely generated groups
- On multidimensional Schur rings of finite groups
- A classification of the prime graphs of pseudo-solvable groups
- On generations by conjugate elements in almost simple groups with socle 2𝐹4(𝑞2)′
- A characterization of the simple Ree groups 2𝐹4(𝑞2) by their character codegrees
- A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters
- Class-two quotients of finite permutation groups
- A note on 𝑑-maximal 𝑝-groups
