Journal article icon

Journal article

Concise presentations of direct products

Abstract:
Direct powers of perfect groups admit more concise presentations than one might naively suppose. If H1(G;Z) = H2(G;Z) = 0, then Gn has a presentation with O(log n) generators and O(log n)3 relators. If, in addition, there is an element g 2 G that has infinite order in every non-trivial quotient of G, then Gn has a presentation with d(G) + 1 generators and O(log n) relators. The bounds that we obtain on the deficiency of Gn are not monotone in n; this points to potential counterexamples for the Relation Gap Problem.
Publication status:
Published
Peer review status:
Peer reviewed

Actions


Access Document


Files:
Publisher copy:
10.1090/proc/13991

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
More from this funder
Funding agency for:
Bridson, M
Grant:
Wolfson Research Merit Award
Publisher:
American Mathematical Society Publisher's website
Journal:
Proceedings of the American Mathematical Society Journal website
Volume:
150
Pages:
1361-1368
Publication date:
2022-01-24
Acceptance date:
2017-10-06
DOI:
EISSN:
1088-6826
ISSN:
0002-9939
Source identifiers:
736366
Language:
English
Keywords:
Pubs id:
pubs:736366
UUID:
uuid:c0c95a8f-e731-492b-bd2e-af4d0e1904e6
Local pid:
pubs:736366
Deposit date:
2017-10-16

Terms of use


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP