The conjugacy class structure of the Qd(p) groups

Authors

• Colin McKenzie L, Stephen F Austin State UniversityFollow
• Jane H. Long, Stephen F Austin State UniversityFollow

Document Type

Project

Publication Date

Summer 2026

Publication Title

New York Journal of Mathematics

Abstract

In this paper, we provide a classification of the conjugacy classes in the special affine group Qd(p) = (Z_p x Z_p) \semidirect SL(2,p) for odd primes. We use the known conjugacy class structure in SL(2,p) to lift elements to their conjugacy class in Qd(p). More specifically, for an element in Qd(p), its conjugacy class depends on whether the matrix component of the element is the identity, has eigenvalue 1, which is split into two classes in SL(2,p), or whether it lies in some other conjugacy class in SL(2,p). In addition, we provide formulas, in terms of p, for both the number and sizes of conjugacy classes in Qd(p).

ISBN

1076-9803/2026

Repository Citation

L, Colin McKenzie and Long, Jane H., "The conjugacy class structure of the Qd(p) groups" (2026). Faculty Publications. 33.
https://scholarworks.sfasu.edu/mathandstats_facultypubs/33