2011 Fiscal Year Final Research Report
Research on semiregular relative difference sets of(u,λ)-type
| Project/Area Number |
21540021
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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 |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
CHIGIRA Naoki 熊本大学, 自然科学研究科, 准教授 (40292073)
WATANABE Atsumi 熊本大学, 自然科学研究科, 教授 (90040120)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 差集合 / デザイン / 有限幾何 / 有限群 |
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| Research Abstract |
A. Blokhuis et al. have shown that abelian semiregular relative difference sets with lambda=1 are p-groups for some prime p. In this research we study the case lambda=2 and show that the corresponding groups are 2-groups with some exceptions. Concerning the group G=Zp×Zp×Zp, we characterize the known semiregular relative difference sets in G by using functions from Zp to Zp. We also consider generalized Hadamard matrices and give their modification. As an application we construct new generalized Hadamard matrices related to spreads.
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