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SCHUR’S COLOURING THEOREM FOR NONCOMMUTING PAIRS
Published online by Cambridge University Press: 11 April 2019
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
$xy\neq yx$. We show that
$c(G)\rightarrow 0$ if and only if
$k(G)\rightarrow \infty$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 446 - 452
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
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