Deeply concatenable subgroups might never be free

Samuel M. Corson; Saharon Shelah

doi:10.2969/jmsj/80498049

Deeply concatenable subgroups might never be free

Samuel M. Corson, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	1123-1136
Number of pages	14
Journal	Journal of the Mathematical Society of Japan
Volume	71
Issue number	4
DOIs	https://doi.org/10.2969/jmsj/80498049
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 The Mathematical Society of Japan

Keywords

Axiom of choice
Baire property
Free group
Fundamental group
Length function
Strongly bounded group

Access to Document

10.2969/jmsj/80498049

Cite this

@article{339c5ffe5a764bb6a01d6203dc084209,

title = "Deeply concatenable subgroups might never be free",

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

keywords = "Axiom of choice, Baire property, Free group, Fundamental group, Length function, Strongly bounded group",

author = "Corson, {Samuel M.} and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2019 The Mathematical Society of Japan",

year = "2019",

doi = "10.2969/jmsj/80498049",

language = "אנגלית",

volume = "71",

pages = "1123--1136",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

number = "4",

}

TY - JOUR

T1 - Deeply concatenable subgroups might never be free

AU - Corson, Samuel M.

AU - Shelah, Saharon

PY - 2019

Y1 - 2019

N2 - 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 and the Hawaiian earring group. Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups are also presented.

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

KW - Axiom of choice

KW - Baire property

KW - Free group

KW - Fundamental group

KW - Length function

KW - Strongly bounded group

UR - http://www.scopus.com/inward/record.url?scp=85075536190&partnerID=8YFLogxK

U2 - 10.2969/jmsj/80498049

DO - 10.2969/jmsj/80498049

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85075536190

SN - 0025-5645

VL - 71

SP - 1123

EP - 1136

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 4

ER -

Deeply concatenable subgroups might never be free

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this