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- W1963955639 abstract "We investigate ( m , n , k , λ 1 , λ 2 )-divisible difference sets in an abelian group admitting −1 as a multiplier. For the reversible case, we show that this assumption implies severe restrictions on the structure of divisible difference sets. In particular, if ( λ 1 − λ 2 ) n + k − λ 1 is not a square, we prove that all the corresponding divisible difference sets can be constructed by using certain partial difference sets. Also, we determine the structure of reversible divisible difference sets if a Sylow subgroup of G is cyclic. As a consequence, we completely characterize all reversible divisible difference sets in cyclic groups. Finally, the case that −1 is a weak multiplier is studied and restrictions on the parameters are obtained. In fact, we show that n must be a power of 2." @default.
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- W1963955639 date "1992-01-01" @default.
- W1963955639 modified "2023-09-25" @default.
- W1963955639 title "Abelian divisible difference sets with multiplier −1" @default.
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- W1963955639 doi "https://doi.org/10.1016/0097-3165(92)90098-f" @default.
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