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An automorphism is an isomorphism from an object to itself, and which also preserves the objects structure .

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Property of IA automorphisms of free groups

For $n \in\mathbb{N}$ define: $X_n=\{x_1,\ldots,x_n\}$, $F(X_n)$ the free group on $X_n$, $\varphi:F(X_n)\to F(X_{n-1})$ an epimorphism defined by $x_i\stackrel{\varphi}{\mapsto} x_i$ for $1\le i\l …
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