1 results
SCHUR’S COLOURING THEOREM FOR NONCOMMUTING PAIRS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 3 / December 2019
- Published online by Cambridge University Press:
- 11 April 2019, pp. 446-452
- Print publication:
- December 2019
-
- Article
- Export citation
-
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 
$k(G)\rightarrow \infty$.
