A note on 𝑑-maximal 𝑝-groups-Reference-Cited by-同舟云学术

A note on 𝑑-maximal 𝑝-groups

Published:2023-07-04 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Aiech Messab¹,Zekraoui Hanifa²,Guerboussa Yassine³

Affiliation:

1. Department of Mathematics , ENSET-Skikda , Skikda , Algeria

2. Department of Mathematics , University Larbi Ben M’hidi , Oum El Bouaghi , Algeria

3. Department of Mathematics , University Kasdi Merbah-Ouargla , Ouargla , Algeria

Abstract

Abstract A finite 𝑝-group 𝐺 is said to be 𝑑-maximal if d ⁢ ( H ) < d ⁢ ( G )

d(H)<d(G)

for every subgroup H < G

H<G

, where d ⁢ ( G )

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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2022-0071/pdf

Reference15 articles.

1. Y. Berkovich, Groups of Prime Power Order. Vol. 1, De Gruyter Exp. Math. 46, Walter de Gruyter, Berlin, 2008.

2. Y. Berkovich and Z. Janko, Groups of Prime Power Order. Vol. 3, De Gruyter Exp. Math. 56, Walter de Gruyter, Berlin, 2011.

3. N. Blackburn, Generalizations of certain elementary theorems on 𝑝-groups, Proc. London Math. Soc. (3) 11 (1961), 1–22.

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.

5. J. González-Sánchez and B. Klopsch, On 𝑤-maximal groups, J. Algebra 328 (2011), 155–166.

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