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First we consider the following subgroup of the symmetric group of degree 7.
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| (1) |
We can factor this permutation over the cosets of H in Symm(7).
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| (2) |
| (3) |
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| (6) |
Next, consider the group of the (2,3)-torus knot, which is an infinite group.
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The following subgroup of G has index in G equal to 3.
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| (8) |
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| (11) |
The alternating group of degree 5 has the following presentation.
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| (12) |