Four-dimensional compact projective planes with doubly transitive action on the fixed pencil |
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Authors: | Hauke Klein |
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Institution: | (1) Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany |
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Abstract: | We consider a four-dimensional compact projective plane =(
,
) whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil × R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag pW, acts transitively on
p
\{W}, and fixes no point in the set W{p}. We study the actions of and N on
and on the pencil
p
\{W}, in the case that does not contain a three-dimensional elation group. In the special situation that acts doubly transitively on
p
{W}, we will determine all possible planes . There are exactly two series of such planes. |
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Keywords: | 51H10 51H20 51A35 |
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