I am truly lost as to what this problem is asking. I did post this on another forum and received what my have been wonderful advice. However, even after multiple hours and many "Google" searches I am still confused. Please anyone....
The problem states: If $\sigma$ is a permutation of a set $A$, we say that $\sigma$ moves $a\in A$ iff $\sigma(a)\neq a$.
For the symmetric group $S_{36}$ of all permutations of 36 elements, let $H$ be a subset of $S_{36}$ containing all permutations that move no more than four elements. Is $H$ a subgroup of $S_{36}$? Prove.
I am not looking for an answer but more an explanation of what the problem is saying. I do not know what "move no more than four elements" means. I am feeling really stupid. Any help appreciated.