Annali di Matematica Pura ed Applicata

, Volume 158, Issue 1, pp 33–50 | Cite as

Spreads and classes of maximal subgroups ofGL n (q),SL n (q),PGL n (q) andPSL n (q)

  • R. H. Dye


If r divides n then the points of PG(n−1, q) can be partitioned by the (r−1)-subspaees of a classical spread Sr. The underlying finite geometry of this configuration, in particular the orbits of lines, is used to prove that if r is a proper prime divisor of n then the stabilizers of Sr in PGLn(g) and PSLn(q) are maximal subgroups of PGLn(q) and PSLn(q respectively. Special attention is needed for the case of PSLn(q) when n/r=2 and r divides q− 1. An explicit description is found for the stablizers.


Maximal Subgroup Prime Divisor Explicit Description Finite Geometry Classical Spread 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1991

Authors and Affiliations

  • R. H. Dye
    • 1
  1. 1.School of Mathematics The UniversityEngland

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