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  "body": "\n## Example\n\nLet $G = (\\mathbb{Z}, +)$ be the [[integers|0C4JS9RF5M]] with addition. Define $t : G \\to G$ by $t(u) = u + 1$.\nA [[homomorphism|0HV9Y7WG5R]] sends the identity to the identity. But $t(0) = 1$, and $1$ is not the identity $0$.\nWe can also compute directly: $t(0 + 0) = 1$, but $t(0) + t(0) = 2$.\nThus $t$ is not a homomorphism.\n\n## Remarks\n\n$t$ is a bijection, so a bijection between groups need not be an isomorphism.\n",
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