Schur's colouring theorem for non-commuting pairs

Author: 

Sanders, T

Publication Date: 

11 April 2019

Journal: 

Bulletin of the Australian Mathematical Society

Last Updated: 

2021-04-08T04:01:47.043+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.

Symplectic id: 

959411

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article