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The homology of groups, profinite completions, and echoes of Gilbert Baumslag

Abstract:

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group U such that U has no proper subgroups of finite index and every finitely presented group can be embedded in U. There is no algorithm that can determine whether or not a finitely presentable subgroup of a residually finite, biautomatic group is perfect. For every recursively presented abelian group A, there exists...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1515/9783110638387-003
Publication website:
https://www.degruyter.com/view/title/547517

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
ORCID:
0000-0002-0080-9059
Publisher:
De Gruyter Publisher's website
Pages:
11–28
Publication date:
2020-02-10
Acceptance date:
2019-08-16
Event title:
Elementary Theory of Groups and Group Rings, and Related Topics
Event location:
Fairfield University & Graduate Centre CUNY
Event website:
http://faculty.fairfield.edu/pbaginski/ElementaryTheoryConference2018.html#Festschrift
Event start date:
2018-11-01T00:00:00Z
Event end date:
2018-11-02T00:00:00Z
DOI:
EISBN:
978-3-11-063709-0
Source identifiers:
1055459
ISBN:
978-3-11-063673-4
Language:
English
Keywords:
Pubs id:
pubs:1055459
UUID:
uuid:0d121268-9c7a-484b-86c5-2417d6980b62
Local pid:
pubs:1055459
Deposit date:
2019-09-24

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