Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-03-03365-8
Title: Nonexistence of abelian difference sets: Lander's conjecture for prime power orders
Authors: Leung, K.H. 
Ma, S.L. 
Schmidt, B.
Keywords: Difference set
Field descent
Lander's conjecture
Ryser's conjecture
Issue Date: Nov-2004
Citation: Leung, K.H., Ma, S.L., Schmidt, B. (2004-11). Nonexistence of abelian difference sets: Lander's conjecture for prime power orders. Transactions of the American Mathematical Society 356 (11) : 4343-4358. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-03-03365-8
Abstract: In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order > 4 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 p-subgroup containing a difference set of order divisible by p. We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103613
ISSN: 00029947
DOI: 10.1090/S0002-9947-03-03365-8
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