Adam R. Thomas

activity

20132026

most citedSimple Irreducible Subgroups of Exceptional Algebraic Groups

19 citations · 31 across the 9 of their papers we have counts for

collaborators

15 papers

math.GR2026

Common neighbour conjectures for Saxl graphs fail at every base size

Aluna Rizzoli, Adam R. Thomas

For a finite permutation group, a base is a set of points with trivial pointwise stabiliser, and the generalised Saxl graph records which pairs of points lie together in a base of…

math.GR2023★ 1 cited

Complete reducibility in bad characteristic

Alastair J. Litterick, Adam R. Thomas

Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p > 0$ . This paper continues a long-standing effort to classify the co…

math.GR2022

Complete reducibility and subgroups of exceptional algebraic groups

Alastair J. Litterick, David I. Stewart, Adam R. Thomas

This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$ -complete reducibility, where $G$ is a connected reductive algebraic grou…

math.GR2022

Normalisers of maximal tori and a conjecture of Vdovin

Timothy C. Burness, Adam R. Thomas

Let $G = O^{p^{'}} (G ˉ^{F})$ be a finite simple group of Lie type defined over a field of characteristic $p$ , where $F$ is a Steinberg endomorphism of the ambient simple algebraic g…

math.RT2021

Compact Lie Groups and Complex Reductive Groups

John Jones, Dmitriy Rumynin, Adam Thomas

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corre…

math.GR2021

Representatives for unipotent classes and nilpotent orbits

Mikko Korhonen, David I. Stewart, Adam R. Thomas

Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$ . The classification of the conjugacy classes of unipotent elements of $G (k)$ and ni…

math.GR2021★ 1 cited

A New Maximal Subgroup of $E_{8}$ in Characteristic $3$

David A. Craven, David I. Stewart, Adam R. Thomas

We prove the existence and uniqueness of a new maximal subgroup of the algebraic group of type $E_{8}$ in characteristic $3$ . This has type $F_{4}$ , and was missing from previous lists…

math.GR2020

A note on extremely primitive affine groups

Timothy C. Burness, Adam R. Thomas

Let $G$ be a finite primitive permutation group on a set $Ω$ with nontrivial point stabilizer $G_{α}$ . We say that $G$ is extremely primitive if $G_{α}$ acts primitively on each of its…

math.GR2020

The classification of extremely primitive groups

Timothy C. Burness, Adam R. Thomas

Let $G$ be a finite primitive permutation group on a set $Ω$ with nontrivial point stabilizer $G_{α}$ . We say that $G$ is extremely primitive if $G_{α}$ acts primitively on each of its…

math.GR2018

Reducible subgroups of exceptional algebraic groups

Alastair J. Litterick, Adam R. Thomas

Let $G$ be a simple algebraic group over an algebraically closed field. A closed subgroup $H$ of $G$ is called $G$ -completely reducible ( $G$ -cr) if, whenever $H$ is contained in a…

math.GR2017

On the involution fixity of exceptional groups of Lie type

Timothy C. Burness, Adam R. Thomas

The involution fixity $ifix (G)$ of a permutation group $G$ of degree $n$ is the maximum number of fixed points of an involution. In this paper we study the involution fixity…

math.GR2016

Finite subgroups of simple algebraic groups with irreducible centralizers

Martin W. Liebeck, Adam R. Thomas

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgro…

math.GR2015

Complete Reducibility in Good Characteristic

Alastair J. Litterick, Adam R. Thomas

Let $G$ be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic $p \geq 0$ . A closed subgroup $H$ of $G$ is called $G$ -completely reduc…

math.GR2015★ 10 cited

Irreducible A_1 Subgroups of Exceptional Algebraic Groups

Adam Thomas

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_{1}$ subgroups of exc…

math.GR2013★ 19 cited

Simple Irreducible Subgroups of Exceptional Algebraic Groups

Adam Thomas

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exception…

Common neighbour conjectures for Saxl graphs fail at every base size

Complete reducibility in bad characteristic

Complete reducibility and subgroups of exceptional algebraic groups

Normalisers of maximal tori and a conjecture of Vdovin

Compact Lie Groups and Complex Reductive Groups

Representatives for unipotent classes and nilpotent orbits

A New Maximal Subgroup of E8​ in Characteristic 3

A note on extremely primitive affine groups

The classification of extremely primitive groups

Reducible subgroups of exceptional algebraic groups

On the involution fixity of exceptional groups of Lie type

Finite subgroups of simple algebraic groups with irreducible centralizers

Complete Reducibility in Good Characteristic

Irreducible A_1 Subgroups of Exceptional Algebraic Groups

Simple Irreducible Subgroups of Exceptional Algebraic Groups

A New Maximal Subgroup of $E_{8}$ in Characteristic $3$