Flag-Transitive 2-Designs Arising from Line-Spreads in PG(2n-1,2) |
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Authors: | Akihiro Munemasa |
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Institution: | (1) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan |
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Abstract: | A Singer cycle in GL(n,q) is an element of order q permuting cyclically all the nonzero vectors. Let be a Singer cycle in GL(2n,2). In this note we shall count the number of lines in PG (2n-1,2) whose orbit under the subgroup of index 3 in the Singer group ![lang](/content/n42550x5l5421t77/xxlarge9001.gif) ![sgr](/content/n42550x5l5421t77/xxlarge963.gif) is a spread. The lines constituting such a spread are permuted cyclically by the group ![lang](/content/n42550x5l5421t77/xxlarge9001.gif) 3 , hence gives rise to a flag-transitive 2-(22n
,4,1) design. |
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Keywords: | flag-transitive design projective space affine space singer cycle |
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