Melissa Lee

activity

20152025

most citedThe maximal subgroups of the Monster

9 citations · 14 across the 14 of their papers we have counts for

collaborators

15 papers

math.GR2025

Elusive groups from non-split extensions

Jiyong Chen, Melissa Lee, Dorde Mitrovic +2

A finite transitive permutation group is elusive if it contains no derangements of prime order. These groups are closely related to a longstanding open problem in algebraic graph t…

math.GR2023★ 9 cited

The maximal subgroups of the Monster

Heiko Dietrich, Melissa Lee, Tomasz Popiel

The classification of the maximal subgroups of the Monster $M$ is a long-standing problem in finite group theory. According to the literature, the classification is comple…

math.GR2023

Primitive almost simple IBIS groups with sporadic socle

Melissa Lee

An irredundant base $B$ for a permutation group $G \leq Sym (Ω)$ is an ordered subset of $Ω$ with trivial stabiliser such that no base point is fixed by the stabiliser of it…

math.CO2022

Extremely primitive groups and linear spaces

Melissa Lee, Gabriel Verret

A finite non-regular primitive permutation group $G$ is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied f…

math.GR2022

A classification of finite primitive IBIS groups with alternating socle

Melissa Lee, Pablo Spiga

Let $G$ be a finite permutation group on $Ω$ . An ordered sequence $(ω_{1}, \dots, ω_{ℓ})$ of elements of $Ω$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and…

math.GR2021

Saxl graphs of primitive affine groups with sporadic point stabilisers

Melissa Lee, Tomasz Popiel

Let $G$ be a permutation group on a set $Ω$ . A base for $G$ is a subset of $Ω$ whose pointwise stabiliser is trivial, and the base size of $G$ is the minimal cardinality of a base.…

math.GR2021

$M$ , $B$ and $Co_{1}$ are recognisable by their prime graphs

Melissa Lee, Tomasz Popiel

The prime graph, or Gruenberg--Kegel graph, of a finite group $G$ is the graph $Γ (G)$ whose vertices are the prime divisors of $∣ G ∣$ , and whose edges are the pairs ${p, q}$ for wh…

math.GR2021

On the classification of extremely primitive affine groups

Timothy C. Burness, Melissa Lee

Let $G$ be a finite non-regular primitive permutation group on a set $Ω$ with point stabiliser $G_{α}$ . Then $G$ is said to be extremely primitive if $G_{α}$ acts primitively on each o…

math.RT2020

Regular orbits of quasisimple linear groups II

Melissa Lee

Let $V$ be a finite-dimensional vector space over a finite field, and suppose $G \leq Γ L (V)$ is a group with a unique subnormal quasisimple subgroup $E (G)$ that is absolut…

math.GR2019

Regular orbits of quasisimple linear groups I

Melissa Lee

Let $G \leq GL (V)$ be a group with a unique subnormal quasisimple subgroup $E (G)$ that acts absolutely irreducibly on $V$ . A base for $G$ acting on $V$ is a set of vectors…

math.GR2018★ 4 cited

Bases of quasisimple linear groups

Melissa Lee, Martin W. Liebeck

Let $V$ be a vector space of dimension $d$ over $F_{q}$ , a finite field of $q$ elements, and let $G \leq G L (V) ≅ G L_{d} (q)$ be a linear group. A base of $G$ is a set of vectors whos…

math.CO2016

On $m$ -ovoids of regular near polygons

John Bamberg, Jesse Lansdown, Melissa Lee

We generalise the work of Segre (1965), Cameron - Goethals - Seidel (1978), and Vanhove (2011) by showing that nontrivial $m$ -ovoids of the dual polar spaces $D Q (2 d, q)$ , $DW(2d-1,…

math.CO2016

A relative $m$ -cover of a Hermitian surface is a relative hemisystem

John Bamberg, Melissa Lee

An $m$ -cover of the Hermitian surface $H (3, q^{2})$ of $P G (3, q^{2})$ is a set $S$ of lines of $H (3, q^{2})$ such that every point of $H (3, q^{2})$ lies on exactly $m$ lines of $\mat…

math.CO2015★ 1 cited

A New Infinite Family of Hemisystems of the Hermitian Surface

John Bamberg, Melissa Lee, Koji Momihara +1

In this paper, we construct an infinite family of hemisystems of the Hermitian surface $H (3, q^{2})$ . In particular, we show that for every odd prime power $q$ congruent to $…

math.CO2015

A note on relative hemisystems of Hermitian generalised quadrangles

John Bamberg, Melissa Lee, Eric Swartz

In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space $H (3, q^{2})$ , unifying all known infinite familie…

Elusive groups from non-split extensions

The maximal subgroups of the Monster

Primitive almost simple IBIS groups with sporadic socle

Extremely primitive groups and linear spaces

A classification of finite primitive IBIS groups with alternating socle

Saxl graphs of primitive affine groups with sporadic point stabilisers

M, B and Co1​ are recognisable by their prime graphs

On the classification of extremely primitive affine groups

Regular orbits of quasisimple linear groups II

Regular orbits of quasisimple linear groups I

Bases of quasisimple linear groups

On m-ovoids of regular near polygons

A relative m-cover of a Hermitian surface is a relative hemisystem

A New Infinite Family of Hemisystems of the Hermitian Surface

A note on relative hemisystems of Hermitian generalised quadrangles

$M$ , $B$ and $Co_{1}$ are recognisable by their prime graphs

On $m$ -ovoids of regular near polygons

A relative $m$ -cover of a Hermitian surface is a relative hemisystem