Results in Mathematics

, Volume 37, Issue 3–4, pp 308–314 | Cite as

Transitive Parallelisms

  • Mauro Biliotti
  • Vikram Jha
  • Norman L. Johnson
Research article


In this article, the groups acting on parallelisms in PG(3, q), q = pr, which are generated by collineations of order a p-primitive divisor of q3 − 1 are completely determined. In particular, when the group generated is non-solvable only the groups PSL(2,7) or A7 are possible. If the parallelism is transitive then either it is one of the two regular parallelisms in PG(3,2) or the group is solvable and is contained in гL(1,q3)/Z, where Z denotes the scalar group of order q − 1.

Key words and phrases

Parallelism projective space translation plane 

2000 Mathematics Subject Classification

51E23 20B25 


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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • Mauro Biliotti
    • 1
  • Vikram Jha
    • 2
  • Norman L. Johnson
    • 3
  1. 1.Dipartimento di MatematicaUniversité di LecceLecceItaly
  2. 2.Mathematics DeptCaledonian UniversityGlasgowScotland
  3. 3.University of IowaIowa City

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