Gapplet
Let Mr be the monoid of all maps {1,...,r} -> {1,...,r}. If you input a sequence of elements, the submonoid S of Mr generated by the sequence is computed. You will see that if the generators are invertible, then so are all elements of S. You will also see that the inverse of every invertible element of S belongs to S. Since a monoid each element of which is invertible, is a group, it follows that S is a group whenever the generators are invertible (i.e., permutations).
Input a sequence of elements of Mr, e.g., [1,3,4,5,2], [5,3,2,1,4] in case r = 5 |
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The elements of the submonoid of
Mr generated by the input sequence.
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