The Erdos-Turan problem in infinite groups
| dc.creator | Konyagin, Sergei V. | |
| dc.creator | Lev, Vsevolod F. | |
| dc.date | 2009-01-12 | |
| dc.date.accessioned | 2026-07-07T12:28:27Z | |
| dc.date.available | 2026-07-07T12:28:27Z | |
| dc.description | Let $G$ be an infinite abelian group with $|2G|=|G|$. We show that if $G$ is not the direct sum of a group of exponent 3 and the group of order 2, then $G$ possesses a perfect additive basis; that is, there is a subset $S\subseteq G$ such that every element of $G$ is uniquely representable as a sum of two elements of $S$. Moreover, if $G$ \emph{is} the direct sum of a group of exponent 3 and the group of order 2, then it does not have a perfect additive basis; however, in this case there is a subset $S\subseteq G$ such that every element of $G$ has at most two representations (distinct under permuting the summands) as a sum of two elements of $S$. This solves completely the Erdos-Turan problem for infinite groups. It is also shown that if $G$ is an abelian group of exponent 2, then there is a subset $S\subseteq G$ such that every element of $G$ has a representation as a sum of two elements of $S$, and the number of representations of non-zero elements is bounded by an absolute constant. | |
| dc.identifier | https://arxiv.org/abs/0901.1649 | |
| dc.identifier | http://arxiv.org/abs/0901.1649 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215545 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | The Erdos-Turan problem in infinite groups | |
| dc.type | text |