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Collineation Groups which are Primitive on an Oval of a Projective Plane of Odd Order
Author(s) -
Biliotti Mauro,
Korchmaros Gabor
Publication year - 1986
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-33.3.525
Subject(s) - collineation , projective plane , mathematics , fano plane , invariant (physics) , order (exchange) , group (periodic table) , pure mathematics , projective test , pencil (optics) , combinatorics , projective space , physics , geometry , optics , mathematical physics , finance , quantum mechanics , economics , correlation
It is shown that a projective plane of odd order, with a collineation group acting primitively on the points of an invariant oval, must be desarguesian. Moreover, the group is actually doubly transitive, with only one exception. The main tool in the proof is that a collineation group leaving invariant an oval in a projective plane of odd order has 2‐rank at most three.