Computations in symmetric groups
Let
- Is the element
even or odd? Indicate your reasoning. - Find the order of
. Show all work. - Write
in disjoint cycle form. Show all work.
View code
Let $S_n$ denote the symmetric group on $n$ letters.
\begin{enumerate}[label=\alph*)]
\item Is the element $(1\,2\,3\,4)(2\,5\,3\,4\,6)(1\,5\,3\,2\,4\,7)\in S_7$ even or odd? Indicate your reasoning.
\item Find the order of $(1\,3\,4)(2\,4\,3)(1\,3\,4)\in S_4$. Show all work.
\item Write $(1\,5\,2\,3)(2\,1\,3\,4)(1\,5\,2\,3)^{-1}\in S_5$ in disjoint cycle form. Show all work.
\end{enumerate}