Formal-dual subsets of cyclic groups of prime power order
Formal-dual subsets of cyclic groups of prime power order
复制标题
素数幂阶循环群的形式对偶子集
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发表时间：
2016
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通讯作者：
Robert Schuler
中科院分区：
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作者：
Robert Schuler
我们研究了Cohn，Kumar，Reiher和Schürmann引入的素数幂阶有限循环群上的形式对偶的概念。我们将证明，对于任何奇素数幂阶循环群，以及对于任何22 l +1阶循环群，不存在形式对偶子集的本原对。这部分地证明了前面提到的作者的一个猜想，即具有一对本原形式对偶子集的循环群只有{0}和Z/4 Z。
We study the notion of formal-duality over finite cyclic groups of prime power order as introduced by Cohn, Kumar, Reiher and Schürmann. We will prove that for any cyclic group of odd prime power order, as well as for any cyclic group of order 22l+1, there is no primitive pair of formally-dual subsets. This partially proves a conjecture, made by the priorly mentioned authors, that the only cyclic groups with a pair of primitive formally-dual subsets are {0} and Z/4Z.