Explore BrainMass

Explore BrainMass

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

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 December 24, 2021, 4:53 pm ad1c9bdddf

    Solution Preview

    (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.