✦ LIBER ✦
A Sharp Exponent Bound for McFarland Difference Sets withp=2
✍ Scribed by Siu Lun Ma; Bernhard Schmidt
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 291 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
We show that under the self-conjugacy condition a McFarland difference set with p=2 and f 2 in an abelian group G can only exist, if the exponent of the Sylow 2-subgroup does not exceed 4. The method also works for odd p (where the exponent bound is p and is necessary and sufficient), so that we obtain a unified proof of the exponent bounds for McFarland difference sets. We also correct a mistake in the proof of an exponent bound for (320, 88, 24)-difference sets in a previous paper.
1997 Academic Press DD (&1) =n+*G, where D (&1) := g # D g &1 . For A= g # G a g g # ZG, we will write |A| := g # G a g .