2 Ahlman & Koponen (2015)
Let \(k\in \mathbb N\). An automorphisms of \(\mathbb Z/ k\mathbb Z\) is a bijection \(f\) that preserves addition:
\[ f(x+y)=f(x)+f(y) \]
The additive structure \(\mathbb Z/ k\mathbb Z\) is rigid if it has no nontrivial automorphisms.
The additive structure \(\mathbb Z/ 2\mathbb Z\) is rigid.
Proof
Otherwise \(f(0)=1\) and \(f(1)=0\), but then
\[ 0=f(1)=f(1+0)=f(1)+f(0)=0+1=1. \]
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