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 computer algebra solution to a problem in finite groups.
We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
A cyclically pinched product of free groups which is not residually free.
A family of totally ordered groups with some special properties
Let be a field with a Krull valuation and value group , and let be the valuation ring. Theories about spaces of countable type and Hilbert-like spaces in [1] and spaces of continuous linear operators in [2] require that all absolutely convex subsets of the base field should be countably generated as -modules.By [1] Prop. 1.4.1, the field is metrizable if and only if the value group has a cofinal sequence. We prove that for any fixed cardinality , there exists a metrizable field ...
A Finitely Presented Solvable Group that is not Residually Finite.
A finiteness condition on automorphism groups
A finiteness property and an automatic structure for Coxeter groups.
A flat plane that is not the limit of periodic flat planes.
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 Gel'fand model for a Weyl group of type .
A generalization of a theorem of A. D. Otto.
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 Geometrical Construction for the Polynomial Invariants of some Reflection Groups
2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.
A group theoretical model for mass-splitting
A Jones polynomial for braid-like isotopies of oriented links and its categorification.