Math Help - Algebra Help. Groups..

1. Algebra Help. Groups..

Let <G, *> be a group, x, a, b ∈ G and e is the identify element. Prove that if a2 = e and a*x*a = x3, then x8 = e.

2. Re: Algebra Help. Groups..

Originally Posted by mous99
Let <G, *> be a group, x, a, b ∈ G and e is the identify element. Prove that if a2 = e and a*x*a = x3, then x8 = e.
Prove that $x=ax^3a$. Then, $x^8=x^9x^{-1}=(axa)^3x^{-1}=\ldots=e$.

3. Re: Algebra Help. Groups..

how to prove a*x*a = x3 ?

4. Re: Algebra Help. Groups..

Originally Posted by mous99
how to prove a*x*a = x3 ?
You can't prove a hypothesis.

5. Re: Algebra Help. Groups..

can u show be by step? thankssssss

6. Re: Algebra Help. Groups..

Originally Posted by mous99
can u show be by step? thankssssss
Better, ask me step by step.