Non-tall compact groups admit infinite Sidon sets

Sidon Sets in Groups and Induced Subgraphs of Cayley Graphs

Let S be a subset of a group G. We call S a Sidon subset of the first (second) kind, if for any x, y, Z, WE S of which at least 3 are different, xy ~ ZW (xy I "" zwI , resp.). (For abelian groups, the two notions coincide.) If a has a Sidon subset of the second kind with n elements then every n-vertex graph is an induced subgraph of some Cayley graph of G. We prove that a sufficient condition f...

Infinite Sidon sequences

We give the first explicit construction of an infinite Sidon sequence A with A(x) x for some c > 1/3. Our method allows to take c = √ 2− 1. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to Bh sequences when h ≥ 3. In these case our constructions are not explicit but they give the first improvements on the...

Generalized Sidon sets

We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon. © 2010 Elsevier Inc. All rights reserved. MSC: 11B

Measuring sets in infinite groups

We are now witnessing a rapid growth of a new part of group theory which has become known as “statistical group theory”. A typical result in this area would say something like “a random element (or a tuple of elements) of a group G has a property P with probability p”. The validity of a statement like that does, of course, heavily depend on how one defines probability on groups, or, equivalentl...

Sumsets of Sidon sets