Claude Marion

activity

20132023

most citedDeformation theory and finite simple quotients of triangle groups I

4 citations · 6 across the 9 of their papers we have counts for

collaborators

12 papers

math.GR2023

The pro-supersolvable topology on a free group: deciding denseness

Claude Marion, Pedro V. Silva, Gareth Tracey

Let $F$ be a free group of arbitrary rank and let $H$ be a finitely generated subgroup of $F$ . Given a pseudovariety $V$ of finite groups, i.e. a class of finite groups cl…

math.GR2023

On the closure of cyclic subgroups of a free group in pro-V topologies

Claude Marion, Pedro V. Silva, Gareth Tracey

We determine the closure of a cyclic subgroup $H$ of a free group for the pro-{\bf V} topology when {\bf V} is an extension-closed pseudovariety of finite groups. We show that $H$ …

math.GR2023★ 1 cited

The pro- $k$ -solvable topology on a free group

Claude Marion, Pedro V. Silva, Gareth Tracey

We prove that, given a finitely generated subgroup $H$ of a free group $F$ , the following questions are decidable: is $H$ closed (dense) in $F$ for the pro-(met)abelian topology? i…

math.GR2023

On the pseudovariety of groups $U = p \in P ⋁ Ab (p) * Ab (p - 1)$

Claude Marion, Pedro V. Silva, Gareth Tracey

We introduce the pseudovariety of finite groups $U = p \in P ⋁ Ab (p) * Ab (p - 1)$ , where $P$ is the set of all primes.…

math.GR2018★ 1 cited

Generating maximal subgroups of finite almost simple groups

Andrea Lucchini, Claude Marion, Gareth Tracey

For a finite group $G$ , let $d (G)$ denote the minimal number of elements required to generate $G$ . In this paper, given a finite almost simple group $G$ and any maximal subgroup $H…

math.GR2017

On finite simple images of triangle groups

Sebastian Jambor, Alastair Litterick, Claude Marion

For a simple algebraic group G in characteristic p, a triple (a,b,c) of positive integers is said to be rigid for G if the dimensions of the subvarieties of G of elements of order…

math.GR2017

Varieties of elements of given order in simple algebraic groups

Claude Marion

Given a positive integer $u$ and a simple algebraic group $G$ defined over an algebraically closed field $K$ of characteristic $p$ , we derive properties about the subvariety $G_{[u…

math.GR2017

Alternating and symmetric groups with Eulerian generating graph

Andrea Lucchini, Claude Marion

Given a finite group $G$ , the generating graph $Γ (G)$ of $G$ has as vertices the (nontrivial) elements of $G$ and two vertices are adjacent if and only if they are distinct and gen…

math.GR2014

On irreducible subgroups of simple algebraic groups

Timothy C. Burness, Claude Marion, Donna M. Testerman

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p ⩾ 0$ , let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial…

math.GR2013

Irreducible almost simple subgroups of classical algebraic groups

Timothy Burness, Soumaia Ghandour, Claude Marion +1

Let G be a simple classical algebraic group over an algebraically closed field K of characteristic $p \geq 0$ with natural module W. Let H be a closed subgroup of G and let V be a n…

math.GR2013

Deformation theory and finite simple quotients of triangle groups II

Michael Larsen, Alexander Lubotzky, Claude Marion

This paper is a continuation of our first paper [10] in which we showed how deformation theory of representation varieties can be used to study finite simple quotients of triangle…

math.GR2013★ 4 cited

Deformation theory and finite simple quotients of triangle groups I

Michael Larsen, Alexander Lubotzky, Claude Marion

Let $2 \leq a \leq b \leq c \in N$ with $μ = 1/ a + 1/ b + 1/ c < 1$ and let $T = T_{a, b, c} =< x, y, z : x^{a} = y^{b} = z^{c} = x y z = 1 >$ be the corresponding hyperbolic triangle group. Many papers hav…

The pro-supersolvable topology on a free group: deciding denseness

On the closure of cyclic subgroups of a free group in pro-V topologies

The pro-k-solvable topology on a free group

On the pseudovariety of groups U=p∈P⋁​Ab(p)∗Ab(p−1)

Generating maximal subgroups of finite almost simple groups

On finite simple images of triangle groups

Varieties of elements of given order in simple algebraic groups

Alternating and symmetric groups with Eulerian generating graph

On irreducible subgroups of simple algebraic groups

Irreducible almost simple subgroups of classical algebraic groups

Deformation theory and finite simple quotients of triangle groups II

Deformation theory and finite simple quotients of triangle groups I

The pro- $k$ -solvable topology on a free group

On the pseudovariety of groups $U = p \in P ⋁ Ab (p) * Ab (p - 1)$