arXiv subjects

Filippo Spaggiari

Publications and source records attributed to Filippo Spaggiari.

4 recordsLinked to original sources

arXiv2025

Latin quandles of size $16p$

In this paper we obtain the classification of latin quandles of size $16p$ where $p$ is an odd prime. In particular we have that such quandles are always subdirectly reducible but in some cases for small primes. Specifically, we have that latin quandles of size $16p$ are affine if $p\neq 1 \pmod{3}$ or $p\neq 3,5$. If $p=1\pmod 3$ there are $2$ subdirectly reducible non directly decomposable latin quandles of size $16p$ for every prime with $p=1\pmod{3}$ and there are one subdirectly irreducible latin quandle of size $16p$ for $p=3,5$. We provide explicit constructions as coset quandles for all the quandles mentioned above.

math.GR↗

arXiv2025

On Core Quandles

We characterize several properties of core quandles in terms of the properties of their underlying groups. Specifically, we characterize connected cores providing an answer to an open question in \cite{saito} and present a standard homogeneous representation for them, which allows us to prove that simple core quandles are primitive.

math.GR↗

arXiv2023

Coloring Torus Knots by Conjugation Quandles

In the first part of this paper, we present general results concerning the colorability of torus knots using conjugation quandles over any abstract group. Subsequently, we offer a numerical characterization for the colorability of torus knots using conjugation quandles over some particular groups, such as the matrix groups $GL(2,q)$ and $SL(2,q)$, the dihedral group, and the symmetric group.

math.GR↗

arXiv2022

The mutually normalizing regular subgroups of the holomorph of a cyclic group of prime power order

Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its holomorph. In this work, we find and characterize the regular subgroups of $Hol(G)$ that are mutually normalizing each other in the permutation group $Sym(G)$. We represent such regular subgroups as vertices of a graph, and we connect a pair of them by an edge when they mutually normalize each other. The approach to construct this local normalizing graph relies on the theory of gamma functions, and the final result will contain all the information about the regular subgroups of $Hol(G)$ in a compact form.

math.GR↗