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On non-existence of some difference sets

Adegoke Solomon Osifodunrin ; Division of Mathematics and Sciences, Livingstone College, Salisbury, North Carolina, USA

Sažetak

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.

Ključne riječi

representation; idempotents; Menon-Hadamard-McFarland difference sets; intersection numbers

Hrčak ID:

93278

URI

https://hrcak.srce.hr/93278

Datum izdavanja:

5.12.2012.

Posjeta: 1.105 *