English

Deeply concatenable subgroups might never be free

Group Theory 2020-10-07 v1

Abstract

We show that certain algebraic structures lack freeness in the absence of the axiom of choice. These include some subgroups of the Baer-Specker group Zω\mathbb{Z}^{\omega} and the Hawaiian earring group. Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups are also presented

Keywords

Cite

@article{arxiv.1804.05538,
  title  = {Deeply concatenable subgroups might never be free},
  author = {Samuel M. Corson and Saharon Shelah},
  journal= {arXiv preprint arXiv:1804.05538},
  year   = {2020}
}
R2 v1 2026-06-23T01:24:30.406Z