Daniele Garzoni

activity

20172026

most citedConjugacy classes of derangements in finite groups of Lie type

3 citations · 5 across the 11 of their papers we have counts for

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12 papers · 1 filter

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.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.GR2024

Probabilistic Generation of Finite Almost Simple Groups

Jason Fulman, Daniele Garzoni, Robert M. Guralnick

We prove that if G is a sufficiently large finite almost simple group of Lie type, then given a fixed nontrivial element x in G and a coset of G modulo its socle, the probability t…

math.GR2023★ 3 cited

Conjugacy classes of derangements in finite groups of Lie type

Sean Eberhard, Daniele Garzoni

Let $G$ be a finite almost simple group of Lie type acting faithfully and primitively on a set $Ω$ . We prove an analogue of the Boston--Shalev conjecture for conjugacy classes: the…

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…