Daniele Garzoni

activity

20182026

most citedOn the number of conjugacy classes of a primitive permutation group with nonabelian socle

1 citations · 1 across the 7 of their papers we have counts for

collaborators

11 papers

math.GR2026

On a conjecture of Peter Neumann on fixed points in permutation groups

Daniele Garzoni, Robert M. Guralnick, Martin W. Liebeck

We prove a conjecture of Peter Neumann from 1966, predicting that every finite non-regular primitive permutation group of degree $n$ contains an element fixing at least one point a…

math.NT2025

Irreducibility of the characteristic polynomials of random tridiagonal matrices

Lior Bary-Soroker, Daniele Garzoni, Sasha Sodin

Conditionally on the Riemann hypothesis for certain Dedekind zeta functions, we show that the characteristic polynomial of a class of random tridiagonal matrices of large dimension…

math.GR2024

Derangements in non-Frobenius groups

Daniele Garzoni

We prove that if $G$ is a transitive permutation group of sufficiently large degree $n$ , then either $G$ is primitive and Frobenius, or the proportion of derangements in $G$ is lar…

math.NT2024

On the irreducibility of $f (2^{n}, 3^{m}, X)$ and other such polynomials

Lior Bary-Soroker, Daniele Garzoni, Vlad Matei

Let $f (t_{1}, \dots, t_{r}, X) \in Z [t_{1}, \dots, t_{r}, X]$ be irreducible and let $a_{1}, \dots, a_{r} \in Z ∖ {0, \pm 1}$ . Under a necessary ramification as…

math.GR2022

Probability of generation by random permutations of given cycle type

Sean Eberhard, Daniele Garzoni

Suppose $π$ and $π^{'}$ are two random elements of $S_{n}$ with constrained cycle types such that $π$ has $x n^{1/2}$ fixed points and $y n /2$ two-cycles, and likewise $π^{'}$ has $x' n^{1/…

math.GR2022

Minimal invariable generating sets

Daniele Garzoni, Andrea Lucchini

A subset $S$ of a group $G$ invariably generates $G$ if, when each element of $S$ is replaced by an arbitrary conjugate, the resulting set generates $G .$ An invariable generating s…