Martino Garonzi

activity

20112025

most citedOn the number of cyclic subgroups of a finite group

10 citations · 25 across the 23 of their papers we have counts for

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Showing 2020Show all

5 papers · 1 filter

math.CO2020

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

Simona Bonvicini, Marco Buratti, Martino Garonzi +2

Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems,…

math.GR2020

On the maximal number of elements pairwise generating the symmetric group of even degree

Francesco Fumagalli, Martino Garonzi, Attila Maróti

Let $G$ be the symmetric group of degree $n$ . Let $ω (G)$ be the maximal size of a subset $S$ of $G$ such that $⟨ x, y ⟩ = G$ whenever $x, y \in S$ and $x \neq = y$ and let…

math.GR2020

Finite groups, minimal bases and the intersection number

Timothy C. Burness, Martino Garonzi, Andrea Lucchini

Let $G$ be a finite group and recall that the Frattini subgroup $Frat (G)$ is the intersection of all the maximal subgroups of $G$ . In this paper, we investigate the intersect…

math.GR2020

Alternating groups as products of four conjugacy classes

Martino Garonzi, Attila Maróti

Let $G$ be the alternating group $\mbox{Alt}(n)$ on $n$ letters. We prove that for any $ε > 0$ there exists $N = N (ε) \in N$ such that whenever $n \geq…

math.GR2020

On the Primary Coverings of Finite Solvable and Symmetric Groups

Francesco Fumagalli, Martino Garonzi

A primary covering of a finite group $G$ is a family of proper subgroups of $G$ whose union contains the set of elements of $G$ having order a prime power. We denote with $σ_{0} (G)$ …