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Schur's colouring theorem for noncommuting pairs

Abstract:
For G a finite non-Abelian group we write c(G) for the probability that two randomly chosen elements commute and k(G) for the largest integer such that any k(G)-colouring of G is guaranteed to contain a monochromatic quadruple (x, y, xy, yx) with xy , yx. We show that c(G) → 0 if and only if k(G) → ∞.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/S0004972719000406

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hugh's College
Role:
Author
ORCID:
0000-0003-1809-8248
Publisher:
Cambridge University Press
Journal:
Bulletin of the Australian Mathematical Society More from this journal
Volume:
100
Issue:
3
Pages:
446-452
Publication date:
2019-04-11
Acceptance date:
2019-02-18
DOI:
EISSN:
1755-1633
ISSN:
0004-9727
Language:
English
Keywords:
Pubs id:
pubs:959411
UUID:
uuid:bce9fd92-9853-4b58-867b-26b53446c235
Local pid:
pubs:959411
Source identifiers:
959411
Deposit date:
2019-02-18

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