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

3. Every element of Sn can be written as a product of disjoint cycles. If σ = (i1 i2)(j1 j2)(k1 k2 k3 k4),
with the cycles disjoint, we say that σ has cyclic structure ( )( )( ).
(a) Find all possible cyclic structures in S7. Hint: There are 15.
(b) Using part (a), find all possible orders in S7.
(c) Find all possible orders in A7.

Expert Solution

Colby Messinger answered 2 years ago

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