On non-existence of some difference sets
نویسنده
چکیده
Eric Lander conjectured that if G is an abelian group of order v containing a difference set of order n and p is a prime dividing v and n, then the Sylow p-subgroup of G cannot be cyclic. This paper verifies a version of this conjecture for k < 6500. A special case of this version is the non-existence of Menon-Hadamard-McFarland difference sets in 2-groups. We also give an algorithm that easily verifies this version of Lander’s conjecture and show that some groups do not admit (288, 42, 6) difference sets. AMS subject classifications: 05B10
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تاریخ انتشار 2012