Document Type
Article
Article Version
Publisher's PDF
Publication Date
4-25-2018
Abstract
We show that each of the classes of left-orderable groups and orderable groups is a quasivariety with undecidable theory. In the case of orderable groups, we find an explicit set of universal axioms. We then consider the relationship with the Kaplansky group rings conjecture and show that K, the class of groups which satisfy the conjecture, is the model class of a set of universal sentences in the language of group theory. We also give a characterization of when two groups in K or more generally two torsion-free groups are universally equivalent.
Publication Title
Groups Complexity Cryptology
Repository Citation
Fine, Benjamin; Gaglione, Anthony; Rosenberger, Gerhard; and Spellman, Dennis, "Orderable groups, elementary theory, and the Kaplansky conjecture" (2018). Mathematics Faculty Publications. 58.
https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/58
Published Citation
Fine, B., Gaglione, A., Rosenberger, G., & Spellman, D. (2018). Orderable groups, elementary theory, and the Kaplansky conjecture. Groups Complexity Cryptology, 10(1), 43-52. https://doi.org/10.1515/gcc-2018-0005.
DOI
10.1515/gcc-2018-0005
Peer Reviewed
Comments
© 2018 Walter de Gruyter GmbH, Berlin/Boston
The final publisher PDF has been archived here with permission from the copyright holder.