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A computer algebra solution to a problem in finite groups.

Gert-Martin Greuel (2003)

Revista Matemática Iberoamericana

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 family of totally ordered groups with some special properties

Elena Olivos (2005)

Annales mathématiques Blaise Pascal

Let K be a field with a Krull valuation | | and value group G { 1 } , and let B K 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 K should be countably generated as B K -modules.By [1] Prop. 1.4.1, the field K is metrizable if and only if the value group G has a cofinal sequence. We prove that for any fixed cardinality κ , there exists a metrizable field K ...

A Garside presentation for Artin-Tits groups of type C ˜ n

F. Digne (2012)

Annales de l’institut Fourier

We prove that an Artin-Tits group of type C ˜ 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 C ˜ , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...

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