I am suppose to find the right and left cosets of <(1 2 3),2> in S_3 (+) Z_3
(+) is the External Direct Product sign
I know that 0 1 2 make up Z_3
and I think S_3 is 1 2 3
Then how do I start to solve to find the left and right cosets of <(1 2 3),2> in S_3 (+) Z_3
Please help
So this is how i finished it
((12),0)H={((12),0), ((23),2), ((13),1)}
((123),1)H={((123),1), ((132),0), ((123),2)}
((123),0)H={((123),0), ((132),2), ((123),1)}
((132),1)H= {((132),1), ((123), 0), ((123),1)
And so the left cosets would be
((12),1), ((23), 0), ((13), 2), ((12),2), ((23),1), ((13),0), ((12),0), ((23),2), ((13),1)
And the right cosets are
((123),1), ((132),0), ((123),2), ((123),0), ((132),2), ((132),1)
would this be right???