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 Homomorphism]
+	A \textit{homomorphism} $\phi$ from a group $G$ to a group $\overline{G}$ is a mapping from $G$ into $\overline{G}$ that preserves the group operation; that is, $\phi(ab) = \phi(a)\phi(b)$ for all $a, b$ in $G$.
+\end{definition}
+
+\begin{definition}[Kernel of a Homomorphism]
+	The \textit{kernel} of a homomorphism $\phi$ from a group $G$ to a group with identity $e$ is the set $\{x \in G\ \vert\ \phi(x)=e\}$. The kernel of $\phi$ is denoted by $\ker\phi$.
+\end{definition}