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Strong characterizing sequences for subgroups of compact groups

✍ Scribed by András Biró

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
250 KB
Volume
121
Category
Article
ISSN
0022-314X

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✦ Synopsis

In [A. Biró, V.T. Sós, Strong characterizing sequences in simultaneous Diophantine approximation, J. Number Theory 99 (2003) 405-414] we proved that if Γ is a subgroup of the torus R/Z generated by finitely many independent irrationals, then there is an infinite subset A ⊆ Z which characterizes Γ in the sense that for γ ∈ R/Z we have a∈A aγ < ∞ if and only if γ ∈ Γ . Here we consider a general compact metrizable Abelian group G instead of R/Z, and we characterize its finitely generated free subgroups Γ by subsets A ⊆ G * , where G * is the Pontriagin dual of G. For this case we prove stronger forms of the analogue of the theorem of the above mentioned work, and we find necessary and sufficient conditions for a kind of strengthening of this statement to be true.

📜 SIMILAR VOLUMES

Compact Subgroups of Linear Algebraic Gr
Compact Subgroups of Linear Algebraic Groups
✍ Richard Pink 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 497 KB

The general problem underlying this article is to give a qualitative classification Ž . of all compact subgroups ⌫ ; GL F , where F is a local field and n is arbitrary. It is natural to ask whether ⌫ is an open compact subgroup of H E , where H is a linear algebraic group over a closed subfield E ;