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Groups and FieldsHardPermutation Groups

Permutation Groups · Hard problem

In S6S_6, let σ=(1 3 5)(2 4 6)\sigma=(1\,3\,5)(2\,4\,6) and τ=(1 2)(3 4)(5 6)\tau=(1\,2)(3\,4)(5\,6). Find the permutation xx with xσ=τx\sigma=\tau, and give the order of xx.