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.
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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, $\displaystyle x^8=x^9x^{-1}=(axa)^3x^{-1}=\ldots=e$.
how to prove a*x*a = x3 ?
Originally Posted by mous99 how to prove a*x*a = x3 ? You can't prove a hypothesis.
can u show be by step? thankssssss
Originally Posted by mous99 can u show be by step? thankssssss Better, ask me step by step.
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