arXiv subjects

Giuseppe Nozzi

Publications and source records attributed to Giuseppe Nozzi.

5 recordsLinked to original sources

arXiv2026

Near-Rings and Skew Braces

This paper adapts Rump's correspondence between radical rings and braces to a more general setting, utilizing a suitable class of near-rings. Given a right near-ring $(R,+,\circ)$ with a multiplicative identity, we define a new operation that yields a monoid. Under natural compatibility conditions expressed via a filtration, this monoid becomes a topological group, yielding a topological right skew brace. This generalization recovers radical-ring braces and successfully applies to near-rings of maps under composition. We provide several explicit applications, demonstrating that the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups naturally arise as multiplicative groups of such topological skew braces.

math.GR↗

arXiv2025

Normality conditions in the Sylow $\boldsymbol{p}$-subgroup of $\boldsymbol{\mathrm{Sym}(p^n)}$ and its associated Lie algebra

In this work, we give a description of the structure of the normal subgroups of a Sylow $p$-subgroup $W_n$ of $\mathrm{Sym}(p^n)$, 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 the algebra contexts. Finally, we calculate the growth of the normalizer chain starting from an elementary abelian regular subgroup of $W_n$.

math.GR↗

arXiv2024

Transfinite hypercentral iterated wreath product of integral domains

Starting with an integral domain $D$ of characteristic $0$, we consider a class of iterated wreath product $W_n$ of $n$ copies of $D$. In order that $W_n$ be transfinite hypercentral, it is necessary to restrict to the case of wreath products defined by way of numerical polynomials. We also associate to each of these groups a Lie ring, providing a correspondence preserving most of the structure. This construction generalizes a result of \cite{netreba} which characterizes the Lie algebras associated to the Sylow $p$-subgroups of the symmetric group $\Sym(p^n)$. As an application, we explore the normalizer chain $\lbrace\mathbf{N}_{i}\rbrace_{i\geq -1}$ starting from the canonical regular abelian subgroup $T$ of $W_n$. Finally, we characterize the regular abelian normal subgroups of $\mathbf{N}_0$ that are isomorphic to $D^n$.

math.GR↗

arXiv2024

A classification of module braces over the ring of $\mathbf{p}$-adic integers

In this paper we study the $R$-braces $(M,+,\circ)$ such that $M\cdot M$ is cyclic, where $R$ is the ring of $p$-adic and $\cdot$ is the product of the radical $R$-algebra associated to $M$. In particular, we give a classification up to isomorphism in the torsion-free case and up to isoclinism in the torsion case. More precisely, the isomorphism classes and the isoclinism classes of such radical algebras are in correspondence with particular equivalence classes of the bilinear forms defined starting from the products of the algebras.

math.GR↗

arXiv2024

A classification of $\mathbb{F}_{p^k}$-braces using bilinear forms

Let $\mathbb{F}_{p^k}$ be a finite field of odd characteristic $p$. In this paper we give a classification, up to isomorphism, of the associative commutative $\mathbb{F}_{p^k}$-algebras, starting from the connection with their bi-brace structure. Such classification is the generalization in odd characteristic of the result proved by Civino at al. in characteristic $2$.

math.GR↗