Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Motivation}
+
+\begin{remark}
+	In general, we say that two designs (arrangements of beads) $A$ and $B$ are \textit{equivalent under a group $G$} of permutations of the arrangements if there is an element $\phi$ in $G$ such that $\phi(A) = B$. That is, two designs are equivalent under $G$ if they are in the same orbit of $G$. It follows, then, that the number of nonequivalent designs under $G$ is simply the number of orbits of designs under $G$. (The set being permuted is the set of all possible designs or arrangements.)
+\end{remark}