The higher-dimensional Thompson groups $nV$, for $n \geqslant 2$, were introduced by Brin [‘Presentations of higher dimensional Thompson groups’, J. Algebra 284 (2005), 520–558]. We provide new presentations for each of these infinite simple groups. The first is an infinite presentation, analogous to the Coxeter presentation for the finite symmetric group, with generating set equal to the set of transpositions in $nV$ and reflecting the self-similar structure of n-dimensional Cantor space. We then exploit this infinite presentation to produce further finite presentations that are considerably smaller than those previously known.

Weed scientists regularly attend conferences, symposiums, and workshops to communicate with colleagues about their current weed research programs. Communication of research can be hindered by poor visual aids. Computer programs, film recorders, and color printers have greatly increased the ease of visual aid production but have also increased the opportunity to prepare incomprehensible presentations. The size of the text, the amount of information presented, and the contrast between the text color and background color are the most important factors that affect the legibility of visual aids. Text, tables, and graphs should be short, simple, and legible. Computers and film recorders are not essential to produce good visual aids. The greatest assets in the production of visual aids are common sense, familiarity with the production equipment, sufficient preparation time, and critical assessment of the visual aids well in advance of the presentation date.

In this paper we prove two main results. The first is a necessary and sufficient condition for a semidirect product of a semilattice by a group to be finitely generated. The second result is a necessary and sufficient condition for such a semidirect product to be finitely presented.

Let ξ be the set of all finite groups that have efficient presentations. In this paper we give sufficient conditions for the standard wreath product of two ξ-groups to be a ξ-group.

In this paper we study the factorizable braid monoid (also known as the merge-and-part braid monoid) introduced by Easdown, East and FitzGerald in 2004. We find several presentations of this monoid, and uncover an interesting connection with the singular braid monoid. This leads to the definition of the flexible singular braid monoid, which consists of ‘flexible-vertex-isotopy’ classes of singular braids. We conclude by defining and studying the pure factorizable braid monoid, the maximal subgroups of which are (isomorphic to) quotients of the pure braid group.