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arXiv · 1801.09505

The number of homomorphisms from the Hawaiian earring group

Samuel M. Corson
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Abstract

We show a dichotomy for groups of cardinality less than continuum. The number of homomorphisms from the Hawaiian earring group to such a group $G$ is either the cardinality of $G$ in case $G$ is noncommutatively slender, or the number is $2^{2^{\aleph_0}}$ in case $G$ is not noncommutatively slender. An example of a noncommutatively slender group with nontrivial divisible element is exhibited.

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Samuel M. Corson. 2018-01-29. The number of homomorphisms from the Hawaiian earring group. https://arxiv.org/abs/1801.09505

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