Question

(a) State and prove Cauchy theorem for finite abelian groups.
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Answer 1

Answer:

Theorem 3 (Cauchy's Theorem for Abelian Groups). Let G be an Abelian group of order 1 < |G| = n < ∞. Then, if p is a prime dividing n, we have that there is an element g ∈ G of order p. ... If P(|G|) = 1, then G has prime order, say p, and hence is cyclic, with a generator g of order p.

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