|
|||||
 |
|
|
|
|
|
|
|
The
combinatorics of the generalized and extended symmetric
spaces of $\operatorname{SO}(3,\mathbb{F}_q)$
Raman Aliakseyeu, Natalie Oliven, Ethan Thieme and Ellen Ziliak |
|
Vol. 17 (2024), No. 5, 753–769
|
Abstract |
|
We provide a count for the size of both the generalized and extended symmetric spaces of for all involutions when the characteristic is not equal to 2. In addition we explicitly describe the elements in the extended symmetric space and the fixed point group for both involutions. |
Keywords
generalized symmetric space, special orthogonal group,
finite fields
|
Mathematical Subject Classification
Primary: 20G40, 22E46, 53C35, 57S20
|
Milestones
Received: 15 March 2023
Revised: 8 June 2023
Accepted: 10 June 2023
Published: 21 November 2024
Communicated by Scott T. Chapman
|
Authors |
| Raman Aliakseyeu | |
| Department of Mathematical and
Computational Sciences Benedictine University Lisle, IL United States |
|
| Natalie Oliven | |
| Department of Mathematical and
Computational Sciences Benedictine University Lisle, IL United States |
|
| Ethan Thieme | |
| Department of Mathematical and
Computational Sciences Benedictine University Lisle, IL United States |
|
| Ellen Ziliak | |
| Department of Mathematical and
Computational Sciences Benedictine University Lisle, IL United States |
|
| © 2024 MSP (Mathematical Sciences Publishers). |
