On minimal complements and co-minimal pairs in groups

Abstract: Given two non-empty subsets $W,W'\subseteq G$ in a group $G$, the set $W'$ is said to be a complement to $W$ if $W\cdot W'=G$ and it is minimal if no proper subset of $W'$ is a complement to $W$. The notion was introduced by Nathanson in the course of his study of natural arithmetic analogues of the metric concept of nets in the setting of the integers. A notion stronger than minimal complements is that of a co-minimal pair. A pair of subsets $(W,W')$ is a co-minimal pair if $W\cdot W' = G$ and $W$ is minimal with respect to $W'$ and vice-versa. In this talk we shall mainly concentrate on abelian groups and show some recent developments on the existence and the non-existence of minimal complements and of co-minimal pairs.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.