Journal of the Mathematical Society of Japan

Deeply concatenable subgroups might never be free

Samuel M. CORSON and Saharon SHELAH

Advance publication

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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 $\mathbb{Z}^{\omega}$ and the Hawaiian earring group. Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups are also presented.

Note

The first author was supported by European Research Council grant PCG-336983. The second author was partially supported by European Research Council grant 338821.

Article information

Source
J. Math. Soc. Japan, Advance publication (2019), 14 pages.

Dates
Received: 4 May 2018
First available in Project Euclid: 20 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1553068892

Digital Object Identifier
doi:10.2969/jmsj/80498049

Subjects
Primary: 20K20: Torsion-free groups, infinite rank
Secondary: 03E25: Axiom of choice and related propositions 03E35: Consistency and independence results 03E75: Applications of set theory

Keywords
free group Baire property fundamental group axiom of choice strongly bounded group length function

Citation

CORSON, Samuel M.; SHELAH, Saharon. Deeply concatenable subgroups might never be free. J. Math. Soc. Japan, advance publication, 20 March 2019. doi:10.2969/jmsj/80498049. https://projecteuclid.org/euclid.jmsj/1553068892


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