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Nonexistence of abelian difference sets: Lander's conjecture for prime power orders |
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| Authors: | Ka Hin Leung Siu Lun Ma Bernhard Schmidt |
| Institution: | Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore ; Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore ; Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany |
| Abstract: | In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order  and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander's conjecture which asserts that there is no abelian group with a cyclic Sylow  -subgroup containing a difference set of order divisible by  . We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3. |
| Keywords: | Difference set Ryser's conjecture Lander's conjecture field descent |
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