Abstract
We study commutative Schur rings over the special orthogonal groups $\mathrm{SO}^{\pm}(n,2)$ that contain the class $\mathcal{C}$ of transvections. We show that the partition of $\mathcal{C}$ determined by a commutative Schur ring has either one or two parts. We classify all remaining partitions of $\mathcal{C}$ that could be determined by a commutative Schur ring.
Degree
PhD
College and Department
Mathematics; Computational, Mathematical, and Physical Sciences
Rights
https://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Haviland, Andrew, "Commutative Schur Rings Over Characteristic 2 Special Orthogonal Groups" (2025). Theses and Dissertations. 11127.
https://scholarsarchive.byu.edu/etd/11127
Date Submitted
2025-12-09
Document Type
Dissertation
Keywords
schur ring, symplectic group, orthogonal group, 3-transposition group, characteristic 2, strong Gelfand pair
Language
english