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Cauchy theorem

 Cauchy theorem for finite abelian groups :

 If G is a finite abelian group such that p/ o( G) , p is a prime number , then there exists an element a( ≠ e) ∈ G such that  a^p= e  i.e. o(a) = p.

Cauchy theorem for finite groups :

 If G is a finite group such that p/ o (G)  , p is a prime number , then 

there exists an element of order p in G.

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