# Schur's colouring theorem for non-commuting pairs

Sanders, T

11 April 2019

## Journal:

Bulletin of the Australian Mathematical Society

## Last Updated:

2021-09-26T00:26:19.113+01:00

## 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 not equal to yx. We show that c(G) tends to 0 if and only
if k(G) tends to infinity.

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