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Groups and FieldsEasyPermutation Groups

Permutation Groups · Easy problem

U(8)={1,3,5,7}U(8) = \{1,3,5,7\} under multiplication mod 88 has 44 elements. In the regular representation of U(8)U(8), the permutation λ3 ⁣:x↦3x(mod8)\lambda_3\colon x \mapsto 3x \pmod 8 decomposes into how many disjoint 22-cycles (it has no fixed points)?