Date of Award
2009-01-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Piotr Wojciechowski
Abstract
We will give a definition, examples and basic properties of pseudo-ordered groups. These generalize partially-ordered groups. The pseudo-ordered groups have a compatible pseudo-order relation that may lack transitivity. Unlike partially-ordered groups, our groups can be finite and still admit a non-trivial pseudo-order. We will show necessary and sufficient conditions for a group to have a compatible pseudo-order. We also consider maximal pseudo-orders. We give a definition of a pseudo chain induced by a pseudo-order and characterize all pseudo chains on the group $\mathbb {Z}_{n}.$ We will calculate the number of non-isomorphic pseudo-orders on $\mathbb {Z}_{n}$ for $ n < 24.$
Language
en
Provenance
Received from ProQuest
Copyright Date
2009
File Size
47 pages
File Format
application/pdf
Rights Holder
Maria Dolores Cruz
Recommended Citation
Cruz, Maria Dolores, "Introduction to Pseudo-ordered Groups" (2009). Open Access Theses & Dissertations. 2663.
https://scholarworks.utep.edu/open_etd/2663