2 Ahlman & Koponen (2015)

Definition 10

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Let $k \in N$ . An automorphisms of $Z / k Z$ is a bijection $f$ that preserves addition:

f (x + y) = f (x) + f (y)

Definition 11

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The additive structure $Z / k Z$ is rigid if it has no nontrivial automorphisms.

Theorem 12

The additive structure $Z / 2 Z$ 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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