I just started learning about group orbits, and wanted to look it up online, because I needed some more clarification. However, stumbling upon this Wolfram's Mathworld entry, I ended up even more confused, especially after reading that example for the permutation group G(adsbygoogle = window.adsbygoogle || []).push({}); _{1}. Could someone perhaps explain to me how exactly it is that if [itex]G_{1} = \{(1234), (2134), (1243), (2143)\}[/itex], the orbits of 1 and 2 are {1, 2}? To me it seems that 1 can get sent to either 2, 3 or 4, but not to itself, and 2 to 1, 3 and 4, but I also know that orbits are either disjoint or equal, so I must not be getting something.

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# Group orbits

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