Emilio Pierro

activity

20142020

most citedOn the smallest non-trivial quotients of mapping class groups

4 citations · 13 across the 9 of their papers we have counts for

collaborators

9 papers

math.GR2020

Point-primitive generalised hexagons and octagons and projective linear groups

S. P. Glasby, E. Pierro, Cheryl E. Praeger

We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the pr…

math.CO2020

The order complex of $P G L_{2} (p^{2^{n}})$ is contractible when $p$ is odd

Emilio Pierro

Given a group $G$ , its lattice of subgroups $L (G)$ can be viewed as a simplicial complex in a natural way. The inclusion of $1_{G}, G \in L (G)$ implies that $\mat…

math.GR2020

Hurwitz Generation in Groups of Types $F_{4}$ , $E_{6}$ , $^{2} E_{6}$ , $E_{7}$ and $E_{8}$

Emilio Pierro

A Hurwitz generating triple for a group $G$ is an ordered triple of elements $(x, y, z) \in G^{3}$ where $x^{2} = y^{3} = z^{7} = x y z = 1$ and $⟨ x, y, z ⟩ = G$ . For the finite quasisimple…

math.GR2017★ 2 cited

Doubly Hurwitz Beauville groups

Gareth A. Jones, Emilio Pierro

If $S$ is a Beauville surface $(C_{1} \times C_{2}) / G$ , then the Hurwitz bound implies that $∣ G ∣ \leq 1764 χ (S)$ , with equality if and only if th…

math.GR2017★ 3 cited

The Hurwitz Subgroups of $E_{6} (2)$

Emilio Pierro

We prove that the exceptional group $E_{6} (2)$ is not a Hurwitz group. In the course of proving this, we complete the classification up to conjugacy of all Hurwitz subgroups of $E_6(…

math.GR2017★ 4 cited

On the smallest non-trivial quotients of mapping class groups

Dawid Kielak, Emilio Pierro

We prove that the smallest non-trivial quotient of the mapping class group of a connected orientable surface of genus at least 3 without punctures is $Sp_{2 g} (2)$ , thus co…

math.GR2017★ 3 cited

On the smallest non-abelian quotient of $Aut (F_{n})$

Barbara Baumeister, Dawid Kielak, Emilio Pierro

We show that the smallest non-abelian quotient of $Aut (F_{n})$ is $PSL_{n} (Z /2 Z) = L_{n} (2)$ , thus confirming a conjecture of Mecchia--Zimmer…

math.GR2014

The Möbius function of the small Ree groups

Emilio Pierro

The Möbius function for a group, $G$ , was introduced in 1936 by Hall in order to count ordered generating sets of $G$ . In this paper we determine the Möbius function of the simple…

math.GR2014★ 1 cited

New Examples of Mixed Beauville Groups

Ben Fairbairn, Emilio Pierro

We generalise a construction of mixed Beauville groups first given by Bauer, Catanese and Grunewald. We go on to give several examples of infinite families of characteristically si…

Point-primitive generalised hexagons and octagons and projective linear groups

The order complex of PGL2​(p2n) is contractible when p is odd

Hurwitz Generation in Groups of Types F4​, E6​, 2E6​, E7​ and E8​

Doubly Hurwitz Beauville groups

The Hurwitz Subgroups of E6​(2)

On the smallest non-trivial quotients of mapping class groups

On the smallest non-abelian quotient of Aut(Fn​)

The Möbius function of the small Ree groups

New Examples of Mixed Beauville Groups

The order complex of $P G L_{2} (p^{2^{n}})$ is contractible when $p$ is odd

Hurwitz Generation in Groups of Types $F_{4}$ , $E_{6}$ , $^{2} E_{6}$ , $E_{7}$ and $E_{8}$

The Hurwitz Subgroups of $E_{6} (2)$

On the smallest non-abelian quotient of $Aut (F_{n})$