Question 69
Let $m$ and $n$ be two positive integers such that $n - 1 \gt m \gt 1$, let $S_n$ be the group of the permutations of degree $n$ and let $S$ be the subset of $S_n$ made by all permutations $\sigma$ with the property $\sigma(m) \lt \sigma(m+1) \lt \dots \lt \sigma(n)$. Show that $S$ contains a unique subgroup of $S_n$, which contains all the transpositions from $S_n$ which belong to $S$.
Ioan Băetu
Ioan Băetu