Subsets of finite groups exhibiting additive regularity
Combinatorics
2012-06-26 v1
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.
Cite
@article{arxiv.1206.5569,
title = {Subsets of finite groups exhibiting additive regularity},
author = {Robert S. Coulter and Todd Gutekunst},
journal= {arXiv preprint arXiv:1206.5569},
year = {2012}
}