The classifications of countably-based profinite abelian groups

Details The classifications of countably-based profinite abelian groups The classifications of countably-based profinite abelian groups

2011-01-15

arxiv.org/abs/1101.3005v2

Mathematics

Group Theory

Scientific paper

In the first half of this paper, we outline the construction of a new class of abelian pro-$p$ groups, which covers all countably-based pro-$p$ groups. In the second half, we study them, and classify them up to topological isomorphism and abstract isomorphism. We use Ulm's classification of discrete countable p-groups, which are the Pontryagin duals of such pro-$p$ groups. It emerges that they are all abstractly isomorphic to Cartesian products of finite groups and $p$-adic integers. We have thus constructed uncountably many pairwise topologically non-isomorphic profinite groups abstractly isomorphic to a Cartesian product of cyclic groups.

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