Research on the sumsets of different types of group
Hang Yu · Theoretical and Natural Science · 2023
In this article, author introduce the theories about the sums of sets. First the definitionX ∙ Y = { x_i∙ y_j | x_i ∈ X,y_j∈Y }, that X, Y is a subset of group G. the first relative theorem is prove by Cauchy–Davenport. The beginning is the Kneser’s theory, and then, in the second part, this paper introduces several types of sumsets, though most of them is based on abelian group (commutative group or additive group) and if not, the author gives out the definition. And the popular topic about this is the sum-free sets, but this paper will only introduce a few. Readers who want detailed prove need to look for proves on the reference articles and the theory author talked is a small part of them (important or interesting ones). In some of references, the “+” can be change to other operation which satisfy the group, so this paper changes them into “∙”.