A transitive self-polar double-twenty of planes
1996 ◽
Vol 61
(2)
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pp. 249-257
Keyword(s):
AbstractWe demonstrate the existence, in the 5-dimensional projective space over any field J in which 1 + 1 ≠ 0 and −1 is a square, of a non-degenerate double-twenty of planes (ℋ, K) with the property that there is a group of collineations which acts transitively on ℋ ∪ K while each element of the group either maps ℋ onto itself and K onto itself or else swaps ℋ with K. If there is an involutory automorphism of J which swaps the two square roots of −1, then (ℋ, K) is also self-polar (with respect to a unitary polarity). We describe some of the geometry (in both 5-dimensional and 3-dimensional space) associated with the double-twenty (ℋ, K) and its group.
1978 ◽
Vol 30
(03)
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pp. 483-489
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Keyword(s):
Keyword(s):
2007 ◽
Vol 16
(04)
◽
pp. 489-497
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1996 ◽
Vol 19
(1)
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pp. 99-119
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Keyword(s):
2016 ◽
Vol 73
◽
pp. 221-243
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