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On the Computation of Conjugation Classes of Elements of PGL(3, q)

Year 2022, Volume: 15 Issue: 1, 69 - 74, 30.04.2022

Michael Braun

https://doi.org/10.36890/iejg.977878

Abstract

In this article an explicit list of representatives of all conjugacy classes of the projective linear group $\pgl(3,q)$ is computed with complexity $O(q^2)$.

Keywords

Conjugacy classes projective linear group group action

References

  • [1] Ball, S., Hirschfeld, J.W.P.: Bounds on (n; r)-Arcs and their Application to Linear Codes. Finite Fields and Their Applications. 3, 326–336 (2005).
  • [2] Braun, M.: New Lower Bounds on the Size of (n; r)-Arcs in PG(2; q). Journal of Combinatorial Designs. 27, 682-687 (2019).
  • [3] Hirschfeld, J.W.P., Storme, L.: The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001, pages 201–246. Springer US, Boston, MA. (2001).
  • [4] MacDonald, I.G.: Numbers of Conjugacy Classes in Some Finite Classical Groups. Bulletin of the Australian Mathematical Society. 23, 23–48 (1981).
  • [5] Wall, G.E.: Conjugacy Classes in Projective and Special Linear Groups. Bulletin of the Australian Mathematical Society. 22, 339–364 (1980).

Year 2022, Volume: 15 Issue: 1, 69 - 74, 30.04.2022

Michael Braun

https://doi.org/10.36890/iejg.977878

Abstract

References

  • [1] Ball, S., Hirschfeld, J.W.P.: Bounds on (n; r)-Arcs and their Application to Linear Codes. Finite Fields and Their Applications. 3, 326–336 (2005).
  • [2] Braun, M.: New Lower Bounds on the Size of (n; r)-Arcs in PG(2; q). Journal of Combinatorial Designs. 27, 682-687 (2019).
  • [3] Hirschfeld, J.W.P., Storme, L.: The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001, pages 201–246. Springer US, Boston, MA. (2001).
  • [4] MacDonald, I.G.: Numbers of Conjugacy Classes in Some Finite Classical Groups. Bulletin of the Australian Mathematical Society. 23, 23–48 (1981).
  • [5] Wall, G.E.: Conjugacy Classes in Projective and Special Linear Groups. Bulletin of the Australian Mathematical Society. 22, 339–364 (1980).
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Michael Braun 0000-0001-9816-2216

Early Pub Date April 30, 2022
Publication Date April 30, 2022
Acceptance Date September 8, 2021
Published in Issue Year 2022 Volume: 15 Issue: 1

Cite

APA Braun, M. (2022). On the Computation of Conjugation Classes of Elements of PGL(3, q). International Electronic Journal of Geometry, 15(1), 69-74. https://doi.org/10.36890/iejg.977878
AMA Braun M. On the Computation of Conjugation Classes of Elements of PGL(3, q). Int. Electron. J. Geom. April 2022;15(1):69-74. doi:10.36890/iejg.977878
Chicago Braun, Michael. “On the Computation of Conjugation Classes of Elements of PGL(3, Q)”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 69-74. https://doi.org/10.36890/iejg.977878.
EndNote Braun M (April 1, 2022) On the Computation of Conjugation Classes of Elements of PGL(3, q). International Electronic Journal of Geometry 15 1 69–74.
IEEE M. Braun, “On the Computation of Conjugation Classes of Elements of PGL(3, q)”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 69–74, 2022, doi: 10.36890/iejg.977878.
ISNAD Braun, Michael. “On the Computation of Conjugation Classes of Elements of PGL(3, Q)”. International Electronic Journal of Geometry 15/1 (April 2022), 69-74. https://doi.org/10.36890/iejg.977878.
JAMA Braun M. On the Computation of Conjugation Classes of Elements of PGL(3, q). Int. Electron. J. Geom. 2022;15:69–74.
MLA Braun, Michael. “On the Computation of Conjugation Classes of Elements of PGL(3, Q)”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 69-74, doi:10.36890/iejg.977878.
Vancouver Braun M. On the Computation of Conjugation Classes of Elements of PGL(3, q). Int. Electron. J. Geom. 2022;15(1):69-74.
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