We present an algorithm that, given a subgroup G of the group of the upper triangular matrices with rational entries by a set of generators, computes generators of the lower central series of G. As an application, we show that the constructive membership problem in G can be performed in polynomial time. This draft is intended to be part of a larger project investigating the complexity of comput...

Let γi(G) and Zi(G) denote the i-th terms of the lower and upper central series of a group G, respectively. In 1956 P. Hall showed that if γi+1(G) is finite, then the index |G : Z2i(G)| is finite. We prove that the same result holds under the weaker hypothesis that |γi+1(G) : γi+1(G) ∩ Zi(G)| is finite.

We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexander-type invariants of a finitely generated group and several of the graded Lie...

In order to understand the behaviour of distributed program environments, this paper describes a threedimensional visualization of communications. Most of previous visualizations presented communications by means of two dimensions of time and process, however, three dimensions are required to represent a message intermediary with visualization functions. We make use of a semantic configuration ...

A recent review suggested using topical pharyngeal anaesthesia only in patients who prefer to be endoscoped without sedation. Topical anaesthesia was also found to be unnecessary in sedated patients in a subsequent study'. However the mean (range) dose of midazolam given to patients in this study was 8 mg (4-10). Using a lower dose of midazolam (mean dose = 5.2 mg ± 0.5 (2SEM) ), lignocaine spr...