Recent content by beachbum300

  1. B

    Proving Cauchy's Theorem with induction

    Homework Statement If p is a prime and p divides the order of G where G is a finite abelian group, then G has an element of order p. Prove without using the Fundamenthal Theorem for Finitely Generated Abelian Groups. Hint 1: Induct on the order of G Hint 2: Note that G/H has a smaller...
  2. B

    Prove the following is a group

    Homework Statement Prove that a nonempty set S with an associative binary operation * on S such that a*c=b and d*a=b have solutions in S for all a,b in S is a group. Homework Equations The Attempt at a Solution In order to prove something is a group, I know that I must show...
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