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Concept

Core (group theory)

Related publications (22)

Subgroups of elliptic elements of the Cremona group

Christian Lucius Urech

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...

2021

Structural Properties Of Dendrite Groups

Nicolas Monod

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...

AMER MATHEMATICAL SOC2019

Maximal subgroups acting with two composition factors on irreducible representations of exceptional algebraic groups

Nathan Scheinmann

Let

Y

be a simply connected simple algebraic group over an algebraically closed field

k

of characteristic

p

and let

X

be a maximal closed connected simple subgroup of

Y

. Excluding some small primes in specific cases, we classify the

p

-restrict ...

EPFL2019

Extensive amenability and a Tits alternative for topological full groups

Nóra Gabriella Szoke

This dissertation investigates the amenability of topological full groups using a property of group actions called extensive amenability. Extensive amenability is a core concept of several amenability results for groups of dynamical origin. We study its pr ...

EPFL2019

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Nicolas Monod

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation group ...

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2019

On irreducible subgroups of simple algebraic groups

Donna Testerman, Claude Marion

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 irreducible KG-module, which is p-restricted, tensor indecomposable and rational. Assume that ...

Springer Heidelberg2017

Equivalences between blocks of p-local Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and (K, O, k) be a p-modular system. Let R = O or k. There is a bijection between the blocks of the group algebra and the blocks of the so-called p-local Mackey algebra mu(1)(R)(G). Let b be a block of RG with abelian defect group D ...

Elsevier2015

Trace maps for Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...

Elsevier2015

The torsion group of endotrivial modules

Jacques Thévenaz

Let G be a finite group and let T(G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We determine, in terms of the structure of G, the kernel of the restriction map from T ...

Mathematical Science Publ2015

Homogeneous number of free generators

We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup prope ...

Walter De Gruyter Gmbh2014

The Dade group of a finite group

Caroline Lassueur

The aim of this paper is to construct an equivalent of the Dade group of a p-group for an arbitrary finite group G, whose elements are equivalences classes of endo-p-permutation modules. To achieve this goal we use the theory of relative projectivity with ...

Elsevier2013

Relative Projectivity and Relative Endotrivial Modules

Caroline Lassueur

This dissertation is concerned with modular representation theory of finite groups, and more precisely, with the study of classes of representations, which we shall term relative endotrivial modules. Given a prime number p, a finite group G of order divisi ...

EPFL2012

Endotrivial modules for p-solvable groups

Jacques Thévenaz

We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for p-solvable groups, provided a conjecture can be proved about the case of p-nilpotent groups. ...

2011

Extension groups between simple Mackey functors

In order to better understand the structure of indecomposable projective Mackey functors, we study extension groups of degree 1 between simple Mackey functors. We explicitly determine these groups between simple functors indexed by distinct normal subgroup ...

2009

Counterexamples to a fiber theorem

We exhibit a counterexample to a fiber theorem stated by F. Fumagalli [J. Algebra 283 (2) (2005), 639-654] and show how it affects the rest of Fumagalli's paper. As a consequence, whether the poset A_p(G) is homotopy equivalent to a wedge of spheres for an ...

2009

Elementary abelian subgroups in p-groups of class 2

All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The "geometr ...

EPFL2009

The socle of a projective Mackey functor for a p-group

We study the simple subfunctors of indecomposable projective Mackey functors for a p-group P. Unlike the case of group algebras, the Mackey algebra is not in general self-injective. Thus, the socle of an indecomposable projective functor is not in general ...

2009

Foncteurs de Mackey projectifs

This work deals with the study of projective Mackey functors. Mackey functors are algebraic structures with operations which behave like induction, restriction and conjugation in group representation theory. These objects have properties which generalize m ...

EPFL2008

Aligator: A mathematica package for invariant generation

We describe the new software package Aligator for automatically inferring polynomial loop invariants, The package combines algorithms from symbolic summation and polynomial algebra with computational logic, and is applicable to the rich class of P-solvable ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008

Extrapolation et synthèse

Christian Fiorillo

Let G a locally compact group, H a closed subgroup and 1 < p < ∞. It's well-known that the restriction of the functions from G to H is a surjective linear contraction from Ap(G) onto Ap(H). We prove, when H is amenable, that every element in Ap(H) with com ...

EPFL2007

Related publications (22)

Y

be a simply connected simple algebraic group over an algebraically closed field

k

of characteristic

p

and let

X

be a maximal closed connected simple subgroup of

Y

. Excluding some small primes in specific cases, we classify the

p

-restrict ...

EPFL2019