Date of Award
Fall 2012
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics, Statistics and Computer Science
First Advisor
Pastijn, Francis
Second Advisor
Jones, Peter
Third Advisor
Byleen, Karl
Abstract
In this dissertation we will be focused on determining classes of bands which are embeddable into some band with high symmetry. It is known that rectangular bands have high symmetry and every semilattice is embeddable into a semilattice with high symmetry. We will try to expand on these classes as much as possible.We first discuss properties of classes of semigroups in which every semigroup either has high symmetry or is embeddable into a semigroup with high symmetry. We show that normal bands are embeddable into normal bands with high symmetry and also that the bands, free in the class of all bands that can be embedded in some band with high symmetry, are precisely the free bands.In accordance with techniques in Pastijn (1980), we show an embedding of a normal band into a normal band with high symmetry that preserves much of the original structure. This allows us to look at an embedding of orthodox semigroups for which the band of idempotents is embeddable into a band with high symmetry.We finish the dissertation by showing the result that every band is embeddable into a uniform band. From this, it will then follow that every orthodox semigroup is embeddable into a bisimple orthodox semigroup.