Geodesic
On $(p\sp a,p\sp b,p\sp a,p\sp{a-b})$-relative difference sets
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 3, pp. 279-297.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper provides new exponent and rank conditions for the existence of abelian relative $( p ^{a}, p ^{b}, p ^{a}, p ^{a-b})$-difference sets. It is also shown that no splitting relative ($2 ^{2c},2 ^{d},2 ^{2c},2 ^{2c-d}$)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group $Gncong$ Z $_{8} \times Z _{4} \times Z _{2}$ exists if and only if $exp( G)le$ 4 or $G = Z _{8} \times (Z _{2}) ^{3}$ with $Ncong$ Z $_{2} \times Z _{2}$.
Keywords: relative difference set, exponent bounds, abelian character 
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     author = {Schmidt, Bernhard},
     title = {On $(p\sp a,p\sp b,p\sp a,p\sp{a-b})$-relative difference sets},
     journal = {Journal of Algebraic Combinatorics},
     pages = {279--297},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1997__6_3_a1/}
}
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Schmidt, Bernhard. On $(p\sp a,p\sp b,p\sp a,p\sp{a-b})$-relative difference sets. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 3, pp. 279-297. http://geodesic.mathdoc.fr/item/JAC_1997__6_3_a1/