# Algebra Help. Groups..

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• Oct 19th 2012, 03:10 AM
mous99
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.
• Oct 19th 2012, 04:38 AM
FernandoRevilla
Re: Algebra Help. Groups..
Quote:

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, $x^8=x^9x^{-1}=(axa)^3x^{-1}=\ldots=e$.
• Oct 19th 2012, 07:08 AM
mous99
Re: Algebra Help. Groups..
how to prove a*x*a = x3 ?
• Oct 19th 2012, 07:57 AM
FernandoRevilla
Re: Algebra Help. Groups..
Quote:

Originally Posted by mous99
how to prove a*x*a = x3 ?

You can't prove a hypothesis.
• Oct 19th 2012, 07:59 AM
mous99
Re: Algebra Help. Groups..
can u show be by step? thankssssss
• Oct 19th 2012, 08:15 AM
FernandoRevilla
Re: Algebra Help. Groups..
Quote:

Originally Posted by mous99
can u show be by step? thankssssss

Better, ask me step by step.