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October, 2019 Deeply concatenable subgroups might never be free
Samuel M. CORSON, Saharon SHELAH
J. Math. Soc. Japan 71(4): 1123-1136 (October, 2019). DOI: 10.2969/jmsj/80498049


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.

Funding Statement

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


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Samuel M. CORSON. Saharon SHELAH. "Deeply concatenable subgroups might never be free." J. Math. Soc. Japan 71 (4) 1123 - 1136, October, 2019.


Received: 4 May 2018; Published: October, 2019
First available in Project Euclid: 20 March 2019

zbMATH: 07174398
MathSciNet: MR4023299
Digital Object Identifier: 10.2969/jmsj/80498049

Primary: 20K20
Secondary: 03E25 , 03E35 , 03E75

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

Rights: Copyright © 2019 Mathematical Society of Japan


Vol.71 • No. 4 • October, 2019
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