13335 2.2. SYMMETRIC AND ALTERNATING GROUPS Exercise 52. Compute the orders of the following permutations: • (123) (456). = 3 (135)(13,4). — OBS 15/3/1/4 (135) (13). S • (13) (24) (578). • (13) (249)(5786). 2.2 Symmetric and alternating groups Definition 2.2.1. The set of all permutations over a set X is Sx. Lemma 2.2.2. The set Sx is a group with the combination of Proof. If o and y are permutations over X, then their combinat ermutation (combination of 1-1 and onto functions is again 1- so we know that the combination of function is associative y function that fixes every point is obui nell

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