Abstract
AbstractThe main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) there exists a bi-orderable, two-generated computably presented solvable group with undecidable word problem. Both of the groups can be found among two-generated solvable groups of derived length $3$.(1) [a]nswers a question posed by Downey and Kurtz; (2) answers a question posed by Bludov and Glass in Kourovka Notebook.One of the technical tools used to obtain the main results is a computational extension of an embedding theorem of B. Neumann that was studied by the author earlier. In this paper we also compliment that result and derive new corollaries that might be of independent interest.
Publisher
Cambridge University Press (CUP)
Cited by
6 articles.
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1. Orders on free metabelian groups;Journal of Group Theory;2023-11-30
2. Generic algebraic properties in spaces of enumerated groups;Transactions of the American Mathematical Society;2023-06-22
3. Regular left-orders on groups;Journal of Combinatorial Algebra;2022-11-22
4. On decidability of amenability in computable groups;Archive for Mathematical Logic;2022-03-03
5. Embeddings into left‐orderable simple groups;Journal of the London Mathematical Society;2022-02-16