# n][n]. ForT(o(k)), of T and o. ShowProblem 1: Let n E N and Sn be the set of all bijections r:T, o E Sn denote bythatT O O the composition, k -a) for T σ & S, also ποσ E S,.b) the binary operation o is associativ, i.e., for a, , TE Sn(4 oT) (o ou) oTσοOc) there is a function / E Sn such that for every T E SnLO TTTT = l0 T .Find anexplicit description of : [n] > [n].d) For every o E Sn there is a function TE S withwhere is the bijection in c)e) there is an n E N and o and T withRemark: You just showed that (Sn, o)is a symmetric groupis a non-abelian group. The group Sn

Question
Step 1

The question concerns the group theoretic properties of the symmetric group of order n (the group of permutations of length n).  As per norms, the first three questions are answered

Step 2

Let us give an example of the composition in the case n =3

Step 3

On this set , we define a muliplication operation , using composition of functions. In this example , the compos...

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