Introduction to Order Structures in Groups - Lecture 4

Explore the fourth installment of a comprehensive lecture series on order structures in groups, delivered by Adam Clay as part of the Groupes ordonnés/Orderable Groups workshop. Delve into the various types of total orders on groups and their interactions with standard algebraic structures and constructions, including quotients, free products, and amalgams. Begin with no prior knowledge of group orderings and progressively develop essential tools and structures from the ground up. Examine key concepts such as the dynamical realization of an ordering, the Burns-Hale theorem, Hölder's theorem, and their relationship with local indicability. Discover how even fundamental topics in this field naturally lead to open problems, providing ample opportunities for both novice learners and experienced students to connect with active areas of research in group theory and order structures.