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Equivalence classes of central semiregular relative difference sets. (English) Zbl 0953.05009
In recent years, several authors have investigated semiregular relative difference sets using the notion of cohomology of groups. This concept fits nicely into the theory of relative difference sets since the former is a theory about transversals of a central subgroup \(C\) in a larger group \(E\). Transversals naturally correspond to cocycles. A semiregular relative difference set in \(E\) relative to \(C\) is just a transversal whose corresponding cocycle is orthogonal. The author introduces a new equivalence relation whose classes are finer than the cohomology classes. This new relation seems to be the “correct” relation that one has to use in the investigation of semiregular relative difference sets. It should be noted that cohomology does not preserve orthogonality.

05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
20J06 Cohomology of groups
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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