# Algebra Help. Groups..

• Oct 19th 2012, 02:10 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, 03:38 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 \$\displaystyle x=ax^3a\$. Then, \$\displaystyle x^8=x^9x^{-1}=(axa)^3x^{-1}=\ldots=e\$.
• Oct 19th 2012, 06:08 AM
mous99
Re: Algebra Help. Groups..
how to prove a*x*a = x3 ?
• Oct 19th 2012, 06:57 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, 06:59 AM
mous99
Re: Algebra Help. Groups..
can u show be by step? thankssssss
• Oct 19th 2012, 07:15 AM
FernandoRevilla
Re: Algebra Help. Groups..
Quote:

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

Better, ask me step by step.