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### Permutation group: (1234)=(12)(13)(14)

How do I show in sage that

 (1234)=(12)(13)(14)


I tried:

 PermutationGroup([[(1,2)]]) * PermutationGroup([[(1,3)]]) * PermutationGroup([[(1,4)]])


but sage says:

 For implementing multiplication, provide the method '_mul_' for Permutation Group with generators [(1,2)] resp. Permutation Group with generators [(1,3)]


### Permutation group: (1234)=(12)(13)(14)

How do I show in sage that

 (1234)=(12)(13)(14)


I tried:

 PermutationGroup([[(1,2)]]) * PermutationGroup([[(1,3)]]) * PermutationGroup([[(1,4)]])


but sage says:

 For implementing multiplication, provide the method '_mul_' for Permutation Group with generators [(1,2)] resp. Permutation Group with generators [(1,3)]


But (12) is not a group actually - but permuation. So I tried:

 Permutation([[(1,2)]]) * Permutation([[(1,3)]]) * Permutation([[(1,4)]])


but it gives:

 TypeError: unsupported operand type(s) for -: 'list' and 'int'


### Permutation group: (1234)=(12)(13)(14)

How do I show in sage that

 (1234)=(12)(13)(14)


I tried:tried make use of:

 PermutationGroup([[(1,2)]]) PermutationGroup([1,2]) * PermutationGroup([[(1,3)]]) * PermutationGroup([[(1,4)]])


but sage says:

 For implementing multiplication, provide the method '_mul_' for Permutation Group with generators [(1,2)] resp. Permutation Group with generators [(1,3)]


But (12) is not a group actually - but permuation. So I tried:

 Permutation([[(1,2)]]) * Permutation([[(1,3)]]) * Permutation([[(1,4)]])
PermutationGroup([1,3])


but it gives:doesn't do what is needed.

 TypeError: unsupported operand type(s) for -: 'list' and 'int'