More Abelian groups with free duals
Copyright policy )More Abelian groups with free duals
In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group \mathbb{Z}^\omega is constructed whose dual, Hom (G,\mathbb{Z}) , is free abelian of rank 2^{\aleph_0}. The question of whether \mathbb{Z}^\omega has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of \mathbb{Z}^\omega are noted.
- University of California United States
- University of California, Berkeley United States
dual groups, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, free Abelian groups, Subgroups of abelian groups, topologies, 54A10, Group Theory (math.GR), Torsion-free groups, infinite rank, Mathematical Sciences, 54G99, 510, Direct sums, direct products, etc. for abelian groups, Complementary and Integrative Health, math.GN, FOS: Mathematics, direct sums, math.GR, 20K25, 20K30 (Primary), 20K45, 54A10, 54G99 (Secondary), Mathematics - General Topology, 20K45, Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), 20K25, subgroups of Baer-Specker group, Prevention, Pure mathematics, General Topology (math.GN), Mathematics - Logic, direct products, Pure Mathematics, Subgroups of Z(omega) with whose duals are free abelian of uncountable rank, math.LO, 20K30 (Primary), Topological methods for abelian groups, Logic (math.LO), Mathematics - Group Theory, Peculiar topological spaces
dual groups, Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups, free Abelian groups, Subgroups of abelian groups, topologies, 54A10, Group Theory (math.GR), Torsion-free groups, infinite rank, Mathematical Sciences, 54G99, 510, Direct sums, direct products, etc. for abelian groups, Complementary and Integrative Health, math.GN, FOS: Mathematics, direct sums, math.GR, 20K25, 20K30 (Primary), 20K45, 54A10, 54G99 (Secondary), Mathematics - General Topology, 20K45, Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), 20K25, subgroups of Baer-Specker group, Prevention, Pure mathematics, General Topology (math.GN), Mathematics - Logic, direct products, Pure Mathematics, Subgroups of Z(omega) with whose duals are free abelian of uncountable rank, math.LO, 20K30 (Primary), Topological methods for abelian groups, Logic (math.LO), Mathematics - Group Theory, Peculiar topological spaces
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