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WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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This paper provides new exponent and rank conditions for theexistence of abelian relative (p^a,p^b,p^a,p^a-b)-difference sets. Itis also shown that no splittingrelative (2^2c,2^d,2^2c,2^2c-d)-difference setexists if d c and the forbidden subgroup isabelian. Furthermore, abelian relative (16, 4, 16, 4)-difference setsare studied in detail; in particular, it is shown that a relative(16, 4, 16, 4)-difference set in an abelian group G\not\cong Z_8\times Z_4\times Z_2exists if and onlyif \exp(G)\le 4 or G= Z_8\times ( Z_2)^3with N\cong Z_2\times Z_2.