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    Wilson's Theorem : Cyclic Groups and Order of an Element

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    13.a) If G={g1,g1,....,gr} is an abelian group, show that g1,g2....gr equals the product of the elements of order 2.
    b) Prove Wilson's Theorem: If p is a prime then (p-1)! R (-1)(modp)
    note: R is a equivalence relation

    © BrainMass Inc. brainmass.com October 9, 2019, 3:49 pm ad1c9bdddf
    https://brainmass.com/math/finite-element-method/wilson-s-theorem-cyclic-groups-and-order-of-an-element-14143

    Solution Preview

    Proof:
    (a) G={g1,g2,...,gr} is an abelian group. Suppose A is the set of all the elements of order 2 in G. Let A={a1,a2,...,as}.
    for an element x in A, we have x^2=1 or x=x^(-1). But ...

    Solution Summary

    Wilson's theorem is proven using abelian groups. The proof is concise.

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