# zbMATH — the first resource for mathematics

A new construction of central relative $$(p^a,p^a,p^a,1)$$-difference sets. (English) Zbl 1027.05013
The authors introduce a new construction of central $$(p^a,p^a,p^a,1)$$ relative difference sets (which means that the forbidden subgroup is a central subgroup $$C$$) using orthogonal cocycles defined in terms of linearised permutation polynomials and finite presemifields. This construction yields a wealth of new non-abelian examples, while the case of commutative semifields reduces to a well-known previous construction. The cohomological approach is used to identify equivalence classes of central relative difference sets for which both $$C$$ and $$G/C$$ are elementary abelian. Several small cases are analyzed in detail.

##### MSC:
 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
Full Text: