Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Definition and Examples}
+
+\begin{definition}[Group Isomorphism]
+	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,
+	\[ \phi(ab) = \phi(a)\phi(b),\ \forall a,b \in G \]
+	If there is an isomorphism from $G$ onto $\overline{G}$, we say that $G$ and $\overline{G}$ are \textit{isomorphic} and write $G \approx \overline{G}$.
+\end{definition}