How can i find all the permutations that commute with a given permutation. I know about the trick with multiplying by the inverse of the permutation but i don t know how to apply it? Can someone offer a step by step explanation?
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Since your permutation is written as disjoint cycles, any permutation that commutes with each of these cycles permutes with the entire element. – Arthur Jan 29 '17 at 16:16
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And how can i find what permutations can commute with my disjoint cycles? – Eduard6421 Jan 29 '17 at 17:29
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Well, when does a cycle commute with another permutation? When the other permutation is a power of that cycle, or when the permutation doesn't touch any of the same elements as the cycle. Perhaps even the product of two such permutations. – Arthur Jan 29 '17 at 18:01