Related papers: Truncations of Ordered Abelian Groups

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

This document aims to give a self-contained account of the parts of abelian group theory that are most relevant for algebraic topology. It is almost purely expository, although there are some slightly unusual features in the treatment of…

Computations in the cohomology of finite groups.

We are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in these two directions that can be viewed as improvements on…

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

Presentations for the holomorphs of abelian groups of the form $C_{p^n} \times 1^{m}$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the…

This is the second of three articles on the topic of truncation as an operation on divisible abelian lattice-ordered groups, or simply $\ell$-groups. This article uses the notation and terminology of the first article and assumes its…

This exposition begins with a systematic account of the theory of group schemes, ultimately specializing to algebraic tori.

Every torsion--free abelian group of finite rank has two essentially unique complete direct decompositions whose summands come from specific classes of groups.

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.

This article extends the works of Gon\c{c}alves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of their pure braid group. We get explicit criteria for…

ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

This text consists of the introduction, table of contents, and bibliography of a long manuscript (703 pages) that is currently submitted for publication. This manuscript develops an extension of Garside's approach to braid groups and…

This paper has been withdrawn by the author, since the result was already known.

This article extends the main results of the publication arXiv:2001.01312 to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a…

Recent results on finite open group transformations are reviewed.

A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.

We classify abelian subgroups of two-dimensional Artin groups.

Work in progress concerning alternative formalizations of arithmetic.