The Wreath Product of Powerful p-Groups-Reference-Cited by-同舟云学术

The Wreath Product of Powerful p-Groups

Published:2023-10-27 Issue:11 Volume:15 Page:1987
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Alharbi Bashayer S.¹²^ORCID,Alghamdi Ahmad M.¹^ORCID

Affiliation:

1. Mathematicas Department, Faculty of Sciences, Umm Al-Qura University, Makkah P.O. Box 14035-21955, Saudi Arabia

2. Department of Mathematics, College of Science, Al-Baha University, Alaqiq, Al-Baha P.O. Box 7738-65799, Saudi Arabia

Abstract

This study provides a scholarly examination of fundamental concepts within the field of group theory, specifically focusing on topics such as the wreath product and powerful p-groups. We examine the characteristics pertaining to the structure of the wreath product of cyclic p-groups, with a specific focus on the groups that are powerfully embedded within it. The primary discovery pertains to the construction of the powerful wreath product and the quasi-powerful wreath product. In this study, we establish that subgroups are powerful within the wreath product, specifically focusing on p-groups. The aforementioned outcome is derived from the assumption that p is a prime number and W is the standard wreath product of two nontrivial cyclic p-groups, denoted as G and H.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/11/1987/pdf

Reference26 articles.

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3. Minimal Generating Sets for Some Wreath Products of Groups;Chye;Bull. Aust. Math. Soc.,1973

4. The power-commutator structure of finite p-groups;Arganbright;Pac. J. Math.,1969

5. Powerful p-groups. I. Finite groups;Lubotzky;J. Algebra,1987