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arXiv · 1206.5569

Subsets of finite groups exhibiting additive regularity

Robert S. Coulter·Todd Gutekunst
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Abstract

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In particular, we show that any sum set must exhibit higher-order regularity and that an abelian sum set is necessarily a reversible difference set. We next develop several general construction techniques under the hypothesis that the over-riding group contains a normal subgroup of order 2. Finally, by exploiting properties of dihedral groups and Frobenius groups, several infinite classes of sum sets and partial sum sets are introduced.

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Robert S. Coulter, Todd Gutekunst. 2012-06-25. Subsets of finite groups exhibiting additive regularity. https://arxiv.org/abs/1206.5569

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