Date Thesis Awarded

5-2023

Access Type

Honors Thesis -- Open Access

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Eric Swartz

Committee Members

Pierre Clare

Joshua Gert

Abstract

In this thesis, we study the symmetries of the putative generalized quadrangle of order 6. Although it is unknown whether such a quadrangle Q can exist, we show that if it does, that Q cannot be transitive on either points or lines. We first cover the background necessary for studying this problem. Namely, the theory of groups and group actions, the theory of generalized quadrangles, and automorphisms of GQs. We then prove that a generalized quadrangle Q of order 6 cannot have a point- or line-transitive automorphism group, and we also prove that if a group G acts faithfully on Q such that 259 | |G|, then G is not solvable. Along the way, we develop techniques for studying composite order automorphisms of a generalized quadrangle. Specifically, we deal with automorphisms of order p^k and pq, where p and q are prime.

Recommended Citation

Pesak, Ryan, "Automorphisms of a Generalized Quadrangle of Order 6" (2023). Undergraduate Honors Theses. William & Mary. Paper 1937.
https://scholarworks.wm.edu/honorstheses/1937