pinter-16-A-4-P2-P3

Z3xZ3 : { (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2) }

Z3xZ3 operation table:

      |(0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2)
----------------------------------------------------------------------
(0, 0)|(0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2)
(0, 1)|(0, 1) (0, 2) (0, 0) (1, 1) (1, 2) (1, 0) (2, 1) (2, 2) (2, 0)
(0, 2)|(0, 2) (0, 0) (0, 1) (1, 2) (1, 0) (1, 1) (2, 2) (2, 0) (2, 1)
(1, 0)|(1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2) (0, 0) (0, 1) (0, 2)
(1, 1)|(1, 1) (1, 2) (1, 0) (2, 1) (2, 2) (2, 0) (0, 1) (0, 2) (0, 0)
(1, 2)|(1, 2) (1, 0) (1, 1) (2, 2) (2, 0) (2, 1) (0, 2) (0, 0) (0, 1)
(2, 0)|(2, 0) (2, 1) (2, 2) (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2)
(2, 1)|(2, 1) (2, 2) (2, 0) (0, 1) (0, 2) (0, 0) (1, 1) (1, 2) (1, 0)
(2, 2)|(2, 2) (2, 0) (2, 1) (0, 2) (0, 0) (0, 1) (1, 2) (1, 0) (1, 1)

Z3xZ3 normal proper subgroups:

{ (0, 0) (1, 2) (2, 1) }
{ (0, 0) (1, 1) (2, 2) }
{ (0, 0) (1, 0) (2, 0) }
{ (0, 0) (0, 1) (0, 2) }

----------------------------------------------------------------------
normal subgroup   N = { (0, 0) (1, 2) (2, 1) }

cosets of N:

N+(0, 0) = N+(1, 2) = N+(2, 1) =   { (0, 0) (1, 2) (2, 1) }
N+(0, 1) = N+(1, 0) = N+(2, 2) =   { (0, 1) (1, 0) (2, 2) }
N+(0, 2) = N+(1, 1) = N+(2, 0) =   { (0, 2) (1, 1) (2, 0) }

Z3xZ3/N (all cosets of N):   { N+(0, 0) N+(0, 1) N+(0, 2) }

Z3xZ3/N operation table:

        |N+(0, 0) N+(0, 1) N+(0, 2)
------------------------------------
N+(0, 0)|N+(0, 0) N+(0, 1) N+(0, 2)
N+(0, 1)|N+(0, 1) N+(0, 2) N+(0, 0)
N+(0, 2)|N+(0, 2) N+(0, 0) N+(0, 1)

----------------------------------------------------------------------
normal subgroup   N = { (0, 0) (1, 0) (2, 0) }

cosets of N:

N+(0, 0) = N+(1, 0) = N+(2, 0) =   { (0, 0) (1, 0) (2, 0) }
N+(0, 1) = N+(1, 1) = N+(2, 1) =   { (0, 1) (1, 1) (2, 1) }
N+(0, 2) = N+(1, 2) = N+(2, 2) =   { (0, 2) (1, 2) (2, 2) }

Z3xZ3/N (all cosets of N):   { N+(0, 0) N+(0, 1) N+(0, 2) }

Z3xZ3/N operation table:

        |N+(0, 0) N+(0, 1) N+(0, 2)
------------------------------------
N+(0, 0)|N+(0, 0) N+(0, 1) N+(0, 2)
N+(0, 1)|N+(0, 1) N+(0, 2) N+(0, 0)
N+(0, 2)|N+(0, 2) N+(0, 0) N+(0, 1)

----------------------------------------------------------------------
normal subgroup   N = { (0, 0) (0, 1) (0, 2) }

cosets of N:

N+(0, 0) = N+(0, 1) = N+(0, 2) =   { (0, 0) (0, 1) (0, 2) }
N+(1, 0) = N+(1, 1) = N+(1, 2) =   { (1, 0) (1, 1) (1, 2) }
N+(2, 0) = N+(2, 1) = N+(2, 2) =   { (2, 0) (2, 1) (2, 2) }

Z3xZ3/N (all cosets of N):   { N+(0, 0) N+(1, 0) N+(2, 0) }

Z3xZ3/N operation table:

        |N+(0, 0) N+(1, 0) N+(2, 0)
------------------------------------
N+(0, 0)|N+(0, 0) N+(1, 0) N+(2, 0)
N+(1, 0)|N+(1, 0) N+(2, 0) N+(0, 0)
N+(2, 0)|N+(2, 0) N+(0, 0) N+(1, 0)

----------------------------------------------------------------------
normal subgroup   N = { (0, 0) (1, 1) (2, 2) }

cosets of N:

N+(0, 0) = N+(1, 1) = N+(2, 2) =   { (0, 0) (1, 1) (2, 2) }
N+(0, 1) = N+(1, 2) = N+(2, 0) =   { (0, 1) (1, 2) (2, 0) }
N+(0, 2) = N+(1, 0) = N+(2, 1) =   { (0, 2) (1, 0) (2, 1) }

Z3xZ3/N (all cosets of N):   { N+(0, 0) N+(0, 1) N+(0, 2) }

Z3xZ3/N operation table:

        |N+(0, 0) N+(0, 1) N+(0, 2)
------------------------------------
N+(0, 0)|N+(0, 0) N+(0, 1) N+(0, 2)
N+(0, 1)|N+(0, 1) N+(0, 2) N+(0, 0)
N+(0, 2)|N+(0, 2) N+(0, 0) N+(0, 1)

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