On T-sequences and characterized subgroups

2009/02/04 by Saak Gabriyelyan, Gabriyelyan, S. S. · 1 citation
Computer Science · Engineering · Mathematics · #22-xx #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #General Topology (math.GN) #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0902.0723

openalex publication_date 2009/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a compact metrizable abelian group and u=\u_n\ be a sequence in its dual X^\wedge. Set s_u (X)= \x: (u_n,x)→ 1\ and \mathbbT₀^H = \(z_n)∈ \mathbbT^∞ : z_n→ 1 \. Let G be a subgroup of X. We prove that G=s_u (X) for some u iff it can be represented as some dually closed subgroup G_u of \rm Cl_X G × \mathbbT₀^H. In particular, s_u (X) is polishable. Let u=\u_n\ be a T-sequence. Denote by (\widehatX, u) the group X^\wedge equipped with the finest group topology in which u_n → 0. It is proved that (\widehatX, u)^\wedge =G_u and n (\widehatX, u) = s_u (X)^⊥. We also prove that the group generated by a Kronecker set can not be characterized.

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