# Beginning Abstract Algebra Problem

• September 17th 2010, 10:07 PM
jzellt
Beginning Abstract Algebra Problem
Prove this is true for every group G, or give a counter example to show this is false in some groups:

If x^2 = a^2, then x=a
• September 17th 2010, 10:35 PM
Failure
Quote:

Originally Posted by jzellt
Prove this is true for every group G, or give a counter example to show this is false in some groups:

If x^2 = a^2, then x=a

Obviously, you need a counterexample to $x^2=a^2\Rightarrow x=a$. - What about $\mathbb{R}\backslash\{0\}$ with multiplication?
• September 18th 2010, 07:13 AM
HallsofIvy
Another, simpler, example is the set {1, -1} with multiplication as operation. Yet, another, the Klein 4-group. In fact, any finite group whose order is even!