TITLE: Multiplication in Permutation Groups Written in Cyclic Notation
QUESTION [51 upvotes]: I didn't find any good explanation how to perform multiplication on permutation group written in cyclic notation. For example, if
$$
  a=(1\,3\,5\,2),\quad b=(2\,5\,6),\quad c=(1\,6\,3\,4),
$$ 
then why does $ab=(1\,3\,5\,6)$ and $ac=(1\,6\,5\,2)(3\,4)$?

REPLY [3 votes]: There is a small example on this page . Basically multiplication of permutation groups is applying permutations from right to left on an unaltered sequence.