Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free

Gaussian Groups Are Torsion Free

Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...

Witt groups and torsion Picard groups of smooth real curves

The Witt group of smooth real projective curves was first computed by Knebusch in [Kn]. If the curve is not complete but still smooth, the Witt group is also studied in [Kn] but not explicitely calculated. However, for some precise examples of smooth affine curves, we may find explicit calculations ([Knu] and [Ay-Oj]). In this paper, the Witt group of a general smooth curve is explicitely calcu...

On the Restriction of Characters of Special Linear Groups of Dimension Three

Torsion in Profinite Completions of Torsion-free Groups

LET G be a residually-finite torsion-free group. Is Gthe profinite completion of G-torsion free? This question was asked in [CKL] where it was shown that if G is a finitely generated metabelian-by-finite group then indeed G is torsion free. On the other hand Evans [E] showed that if G is not finitely generated then it is possible that G has torsion. His example is also metabelian. In this note ...

On the Dimension of Matrix Representations of Finitely Generated Torsion Free Nilpotent Groups

It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into GLn(Z) for an appropriate n ∈ N; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [6]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced ...