Permutations avoiding arithmetic patterns
Journal article, 2004
A permutation $\pi$ of an abelian group $G$ (that is, a bijection from $G$ to itself) will be said to avoid
arithmetic progressions if there does not exist any triple $(a,b,c)$ of elements of $G$, not all equal, such that $c-b=b-a$ and $\pi(c)-\pi(b)=\pi(b)-\pi(a)$. The basic question is, which abelian groups possess such a
permutation ? This and problems of a similar nature will be considered.