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Line 87: The order of a permutation is the least common multiple of its cycles' lengths, and the signature is 1 if a permutation has an even number of cycles with an even number of elements, and -1 otherwise. For a summary of the mathematics discussed here, and a demonstration of the manual method for multiplying permutations in cycle notation, I suggest the Socratica YouTube video [https://youtu.be/MpKG6FmcIHk Cycle Notation of Permutations] - Abstract Algebra)]. (Other suitable videos are also available, including the first three parts of [https://youtube.com/playlist?list=PL2k-dbnrYA2h_T8BW42rOiSlGqV3UG-qk this YouTube playlist] by Dr Angela Berardinelli.)

Cycles of a permutation: Difference between revisions

Cycles of a permutation (view source)