Unsolved problems in ordered and orderable groups
V. V. Bludov, A. M. W. Glass, V. M. Kopytov, N. Ya. Medvedev
TL;DR
This paper compiles and updates a list of unsolved problems in ordered and orderable groups, highlighting progress, solutions, and encouraging further research in the field.
Contribution
It provides a comprehensive, updated collection of open problems in ordered groups, including recent progress and solutions, serving as a resource for future research.
Findings
Some problems have been solved with referenced solutions.
Progress has been made on several open problems.
New problems have been added to the original list.
Abstract
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and references provided. A few have been solved and their solutions are noted and referenced. We hope that this submission will act as a spur to mathematicians to solve some of them!
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · semigroups and automata theory