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 and the Hawaiian earring group. Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups are also presented
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}
}