Work

Normality conditions in the Sylow p-subgroup of Sym(p) and its associated Lie algebra

Year: 2025

Type: article

Abstract: In this work, we give a description of the structure of the normal subgroups of a Sylow p -subgroup W n of Sym ( p n ) , showing that they contain a term from the lower central series with bounded index. To this end, we explicitly determine the terms of the upper and the lower central series of W n . We provide a similar description of these series in the Lie algebra associated to W n , giving a new proof of the equality of their terms in both the group and algebra contexts. Finally, we calculate the growth of the normalizer chain starting from an elementary abelian regular subgroup of W n .

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.10.033

Authors: Riccardo Aragona, Norberto Gavioli, Giuseppe Nozzi

Institution: University of L'Aquila

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, Ministero dell'Università e della Ricerca, Ministero dell'Istruzione e del Merito