Embeddings of locally compact abelian p-groups in Hawaiian groups

We show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

Automated summary

This research shows that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four, providing a new geometric interpretation for the classification of locally compact abelian groups rich in commuting closed subgroups. By introducing the idea of algebraic topology for topologically modular locally compact groups through the geometry of the Hawaiian earring, applications for locally compact groups that are noncompact are found.