Created the Abstract Algebra theorems and definitions cheat sheet

part-2/chapters/chapter-10/the-first-isomorphism-theorem.tex

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+\section{The First Isomorphism Theorem}
+
+\begin{theorem}[First Isomorphism Theorem (Jordan, 1870)]
+	Let $\phi$ be a group homomorphism from $G$ to $\overline{G}$. Then the mapping from $G/\ker\phi$ to $\phi(G)$, given by $g\ker\phi \to \phi(g)$, is an isomorphism. In symbols, $G/\ker\phi \approx \phi(G)$.
+\end{theorem}
+
+\begin{corollary}
+	If $\phi$ is a homomorphism from a finite group $G$ to $\overline{G}$, then $\abs{\phi(G)}$ divides $\abs{G}$ and $\abs{\overline{G}}$.
+\end{corollary}
+
+\begin{theorem}[Normal Subgroups Are Kernels]
+	Every normal subgroup of a group $G$ is the kernel of a homomorphism of $G$. In particular, a normal subgroup $N$ is the kernel of the mapping $g \to gN$ from $G$ to $G/N$.
+\end{theorem}