Galois on Nostr: Let’s G be a set and • : G x G -> G an application (named *composition law*). A ...

Let’s G be a set and • : G x G -> G an application (named *composition law*). A *#group * is a pair (G,•) such that :
i) It exists e such that : For all x in G, x•e = e•x = x (neutral element)
ii) For all x in G, it exists y in G such that : x•y = y•x = e. We denoted y by x^{-1}, x inverse. (Inverse)
iii) For all x, y, z in G (x•y)•z = x•(y•z). This property is called associativity.

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