On Unitary Polarities of Finite Projective Planes
1971 ◽
Vol 23
(6)
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pp. 1060-1077
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Keyword(s):
A unitary polarity of a finite projective plane of order q2 is a polarity θ having q3 + 1 absolute points and such that each nonabsolute line contains precisely q + 1 absolute points. Let G(θ) be the group of collineations of centralizing θ. In [15] and [16], A. Hoffer considered restrictions on G(θ) which force to be desarguesian. The present paper is a continuation of Hoffer's work. The following are our main results.THEOREM I. Let θ be a unitary polarity of a finite projective planeof order q2. Suppose that Γ is a subgroup of G(θ) transitive on the pairs x, X, with x an absolute point and X a nonabsolute line containing x. Thenis desarguesian and Γ contains PSU(3, q).
1964 ◽
Vol 7
(4)
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pp. 549-559
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1970 ◽
Vol 22
(4)
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pp. 878-880
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2001 ◽
Vol 25
(12)
◽
pp. 757-762
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1965 ◽
Vol 17
◽
pp. 977-1009
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Keyword(s):
1967 ◽
Vol 19
◽
pp. 376-393
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1984 ◽
Vol 96
(1-2)
◽
pp. 95-96
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1976 ◽
Vol 41
(2)
◽
pp. 391-404
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1978 ◽
Vol 25
(1)
◽
pp. 19-24
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Keyword(s):