2011 Fiscal Year Final Research Report
Finite projective planes and symmetric divisible designs
| Project/Area Number |
21540139
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Oita University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 対称横断デザイン / 対称分割デザイン / 一般アダマール行列 / 有限射影平面 |
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| Research Abstract |
We proved that the order of an automorphism group of any symmetric transversal design STD_2[12 ; 6] is 2^α3^β for some nonnegative integers α and β. We proved that ifπis a projective plane of order 12 admitting a collineation group G of order 9, then G is an elementary abelian group andπis not planar. We classified STD_6[18 ; 3]'s and STD_7[21 ; 3]'s that have a semiregular nonisomorphic automorphism group of order 9 on both points and blocks containing an elation of order 3. We showed that the number of nonisomorphic STD_8[24 ; 3]'s is at least 24.
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