Euler Characteristic and Characters of Discrete Groups.
Euler Characteristics of Groups.
Every -group with all subgroups normal-by-finite is locally finite
A group has all of its subgroups normal-by-finite if is finite for all subgroups of . The Tarski-groups provide examples of -groups ( a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a -group with every subgroup normal-by-finite is locally finite. We also prove that if for every subgroup of , then contains an Abelian subgroup of index at most .
Every braid admits a short sigma-definite expression
A result by Dehornoy (1992) says that every nontrivial braid admits a -definite expression, defined as a braid word in which the generator with maximal index appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new...
Every Cotorsion-free Algebra is an Endomorphism Algebra.
Every Finite Complex has the Homology of a Duality Group.
Examples of highly transitive permutation groups
Excedance number for involutions in complex reflection groups.
Exceptional groups of Lie type as Galois groups.
Exemples de nil-algèbres et de groupes infinis
Existentially closed -groups
Existentially Closed Locally Finite Central Extensions: Multipliers and Local Systems.
Expansion and random walks in : I
We prove that the Cayley graphs of are expanders with respect to the projection of any fixed elements in generating a Zariski dense subgroup.
Expansion and random walks in : II
Expansion in , square-free
Let be a fixed symmetric finite subset of that generates a Zariski dense subgroup of when we consider it as an algebraic group over by restriction of scalars. We prove that the Cayley graphs of with respect to the projections of is an expander family if ranges over square-free ideals of if and is an arbitrary numberfield, or if and .
Experimenting with infinite groups. I.
Explicit presentations for exceptional braid groups.
Explicit resolutions for the binary polyhedral groups and for other central extensions of the triangle gorups.
Explicit solutions to embedding problems associated to orthogonal Galois representations.
Explizite Präsentation gewisser Hilbertscher Modulgruppen durch Erzeugende und Relationen.