Given cyclic permutations: σ=(123),σ2=(45), then what are the inverse cycles σ−1, σ2−1

Question

Given cyclic permutations:  σ=(123),σ2=(45),    then what are the inverse cycles σ−1, σ2−1

Melinda McCombs · Accepted Answer

To find the inverse of a permutation just write it backwards. If τ=(1243)(67) then τ−1=(76)(3421) which can then be rewritten as τ−1=(1342)(67).    For the question: (123)−1=(321)=(132).

Hector Roberts · Accepted Answer

You have that σ1 is the cycle:    1↦2    2↦3    3↦1    And the incverse cycle will look like:    2↦1    3↦2    1↦3

Given cyclic permutations: σ=(123),σ2=(45), then what are the inverse cycles σ−1, σ2−1

Answered question

Answer & Explanation