Local p-Sidon Sets for Lie Groups

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...

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

Bounds for generalized Sidon sets

Let Γ be an abelian group and g ≥ h ≥ 2 be integers. A set A ⊂ Γ is a Ch[g]-set if given any set X ⊂ Γ with |X | = h, and any set {k1, . . . , kg } ⊂ Γ , at least one of the translates X + ki is not contained in A. For any g ≥ h ≥ 2, we prove that if A ⊂ {1, 2, . . . , n} is a Ch[g]-set in Z, then |A| ≤ (g − 1)1/hn1−1/h + O(n1/2−1/2h). We show that for any integer n ≥ 1, there is a C3[3]-set A ...

Sumsets of Sidon sets

Lie Groups and p-Compact Groups

A p-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of p-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on homotopy theoretic considerations. 1 From compact Lie groups to p-co...