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*any*sense?

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- Thread starter williamaholm
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matt grime

Science Advisor

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'are permutations cyclic groups' is no, since one is an element of a group, and one is a group.

A cyclic group is one generated by a single element.

Given a cycle in S_n it generates a cyclic subgroup, which is a proper subgroup unless n=2.

In usual notation, a cycle is something of the form (abc...d), and any permutation is writable as a product of disjoint cycles, that is cycles that have no common elements. eg (123)(45) is a product of disjoint cycles, but (12)(23) isn't. It is equal to (123).

A cycle with n elements in it has order n.

The product of two disjoint cycles of lengths p and q has order lcm(p,q)

this is enough to find all the elements of S_7 that have order 5.

- #3

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Oh, sorry so unbearable that I have to

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