8 lines
483 B
TeX
8 lines
483 B
TeX
\section{Definition and Examples}
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\begin{definition}[Group Isomorphism]
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An \textit{isomorphism} $\phi$ from a group $G$ to a group $\overline{G}$ is a one-to-one mapping (or function) from $G$ onto $\overline{G}$ that preserves the group operation. That is,
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\[ \phi(ab) = \phi(a)\phi(b),\ \forall a,b \in G \]
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If there is an isomorphism from $G$ onto $\overline{G}$, we say that $G$ and $\overline{G}$ are \textit{isomorphic} and write $G \approx \overline{G}$.
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\end{definition}
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