I was studying permutation group, and I got a doubt, that (12345) can be written as (54)(52)(21)(25)(23)(13) ! Instead of (54)(53)(52)(51). But how this transposition be done .can I do anything ? Can I do in someway?
2026-03-29 03:28:30.1774754910
Product of the cycles of permutation group
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Are you asking whether or not if $(12345)$ can be written as $(54)(52)(21)(25)$? You can compute these and see whether or not this is the case. Note usually with cycle notation we have that unique elements should only appear in the cycle decomposition once.