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  3. 3. every element of sn can be written as a product

3. Every element of Sn can be written as a product of disjoint cycles. If ?...

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Advance Math

3. Every element of Sn can be written as a product of disjointcycles. If ? = (i1 i2)(j1 j2)(k1 k2 k3 k4),
with the cycles disjoint, we say that ? has cyclic structure ( )()( ).
(a) Find all possible cyclic structures in S7. Hint: There are15.
(b) Using part (a), find all possible orders in S7.
(c) Find all possible orders in A7.

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