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Im trying to understand Cayley's Theorem.I have this proof

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I have some questions

What is $Sym(G)$ - I understand that it is a permutation group? How do we get that?

How do we say if $y\in G$ then $g^{-1}y\in G$?

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  • $\begingroup$ $\mathrm{Sym}(G)$ is the set of all permutations, that is bijections $G\rightarrow G$, together with the composition of maps. $\endgroup$ – Hagen Knaf Oct 9 '15 at 6:15
  • $\begingroup$ @HagenKnaf what is composition of maps? $\endgroup$ – techno Oct 9 '15 at 6:25
  • $\begingroup$ Let $f:A\rightarrow B$ and $g:B\rightarrow C$ be two maps. Then their composition $g\circ f$ is the map $A\rightarrow C$ defined by $(g\circ f)(a):=g(f(a))$. $\endgroup$ – Hagen Knaf Oct 9 '15 at 6:31
  • $\begingroup$ @HagenKnaf okay... thanks $\endgroup$ – techno Oct 9 '15 at 9:14

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