-generation of finite simple groups.
(2,3)-generation of the groups PSL6(q)
2010 Mathematics Subject Classification: 20F05, 20D06.We prove that the group PSL6(q) is (2,3)-generated for any q. In fact, we provide explicit generators x and y of orders 2 and 3, respectively, for the group SL6(q).
A block-theory-free characterization of
A characterization of the groups Fi22, Fi23 and F24.
A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A cyclically pinched product of free groups which is not residually free.
A Finitely Presented Solvable Group that is not Residually Finite.
A finiteness property and an automatic structure for Coxeter groups.
A free group acting without fixed points on the rational unit sphere
A Garside presentation for Artin-Tits groups of type
We prove that an Artin-Tits group of type is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...
A generalized Hopf formula for higher homology groups.
A geometric approach to the almost convexity and growth of some nilpotent groups.
A geometric invariant for modules over an Abelian group.
A geometric invariant of discrete groups.
A geometric study of Fibonacci groups.
A natural framing of knots.
A new efficient presentation for and the structure of the groups
is the group presented by . In this paper, we study the structure of . We also give a new efficient presentation for the Projective Special Linear group and in particular we prove that is isomorphic to under certain conditions.
A non-quasiconvex subgroup of a hyperbolic group with an exotic limit set.
A note on torsion-by-nilpotent groups
A numerical invariant for finitely generated groups via actions on graphs.