Damian Sercombe

activity

20152024

most citedRandom generation of associative algebras

1 citations · 2 across the 8 of their papers we have counts for

collaborators

9 papers

math.GR2024

The subgroup structure of pseudo-reductive groups

Michael Bate, Ben Martin, Gerhard Röhrle +1

Let $k$ be a field. We investigate the relationship between subgroups of a pseudo-reductive $k$ -group $G$ and its maximal reductive quotient $G^{'}$ , with applications to the subgroup…

math.GR2024

Maximal subgroups of maximal rank in the classical algebraic groups

Vanthana Ganeshalingam, Damian Sercombe, Laura Voggesberger

Let $k$ be an arbitrary field. We classify the maximal reductive subgroups of maximal rank in any classical simple algebraic $k$ -group in terms of combinatorial data associated to…

math.GR2024

Unipotent normal subgroups of algebraic groups

Damian Sercombe

Let $G$ be an affine algebraic group scheme over a field $k$ . We show there exists a unipotent normal subgroup of $G$ which contains all other such subgroups; we call it the restri…

math.GR2022

A construction of pseudo-reductive groups with non-reduced root system

Michael Bate, Gerhard Röhrle, Damian Sercombe +1

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $B C_{n}$ ; these exist only in cha…

math.GR2021

Maximal connected k-subgroups of maximal rank in connected reductive algebraic k-groups

Damian Sercombe

Let $k$ be any field and let $G$ be a connected reductive algebraic $k$ -group. Associated to $G$ is an invariant first studied by Satake and Tits that is called the index of $G$ (a…

math.RA2020★ 1 cited

Random generation of associative algebras

Damian Sercombe, Aner Shalev

There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we st…

math.RA2020

The length and depth of associative algebras

Damian Sercombe, Aner Shalev

Recently there has been considerable interest in studying the length and the depth of finite groups, algebraic groups and Lie groups. In this paper we introduce and study similar n…

math.GR2018

The length and depth of real algebraic groups

Damian Sercombe

Let $G$ be a connected real algebraic group. An unrefinable chain of $G$ is a chain of subgroups $G = G_{0} > G_{1} > ... > G_{t} = 1$ where each $G_{i}$ is a maximal connected real subgroup of $G_{…

math.GR2015★ 1 cited

A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes

Damian Sercombe

Let $(W, S)$ be a Coxeter system with Davis complex $Σ$ . The polyhedral automorphism group $G$ of $Σ$ is a locally compact group under the compact-open topology. If $G$ is a discret…