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...
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...