Multiplication of Permutation Groups

The page is dedicated to putting simple examples which are pretty rare to find on internet(at least to me).

Recently I was trying to learn multiplication of Permutation groups and Simple method of multiplying permutation groups which I think gives clear insight into what is the meaning of composition of permutation groups, also known as multiplication of permutation groups.

The simplest technique is that I found out while experimenting is

 Write it to full length first without any change made for example for (2,4,6)(1,2)(4,7)

                1     2    3    4    5    6    7

Now (4,7) means permute them so,

                1    2    3    7    5    6    4

Now (1,2) shall be permuted so,

              2   1    3    7    5    6    4

Now(2,4,6) means Replace 2->4, 4->6, 6->2, so

                4    1    3    7    5    2    6

This is the final is between  the first set and  the final set we get from above

            1    2    3    4    5    6    7          

  4    1    3    7    5    2    6

so the cycles we get are (1,4,7,6,2). Done. Simple.

Note: My idea of writing this blog is to share my experience, whatever I found out during experiments and trials. There is no doubt that this all might be known already but I found it myself so I shared it. Please update me if something is amiss.