A Kronecker-Weyl theorem for subsets of abelian groups

Details A Kronecker-Weyl theorem for subsets of abelian groups A Kronecker-Weyl theorem for subsets of abelian groups

2010-12-19

arxiv.org/abs/1012.4177v1

Advances in Mathematics, 226 (2011), 4776-4795

Mathematics

Group Theory

Scientific paper

10.1016/j.aim.2010.12.016

Let N be the set of non-negative integer numbers, T the circle group and c the cardinality of the continuum. Given an abelian group G of size at most 2^c and a countable family F of infinite subsets of G, we construct "Baire many" monomorphisms p: G --> T^c such that p(E) is dense in {y in T^c : ny=0} whenever n in N, E in F, nE={0} and {x in E: mx=g} is finite for all g in G and m such that n=mk for some k in N--{1}. We apply this result to obtain an algebraic description of countable potentially dense subsets of abelian groups, thereby making a significant progress towards a solution of a problem of Markov going back to 1944. A particular case of our result yields a positive answer to a problem of Tkachenko and Yaschenko. Applications to group actions and discrete flows on T^c, diophantine approximation, Bohr topologies and Bohr compactifications are also provided.

Affiliated with

Also associated with

No associations

Rating

A Kronecker-Weyl theorem for subsets of abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Kronecker-Weyl theorem for subsets of abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Kronecker-Weyl theorem for subsets of abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725627