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I have some difficulties proving next statement :

If $A$ is a block for a group $G$ and $a \in A$, show that $A$ is a union of orbits for $G_a$ (where $G_a$ is a stabilizer of a in G ).

I would be very thankful for some advice how to start.

Thanks!

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    @Arturo: Ah, tha$n$ks.2011-06-06

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Hint. If $g\in G_a$, then $gA=A$ (since $ga = a\in gA\cap A$). Therefore, $G_aA = A$.

Now let $b\in A$. The orbit of $b$ for $G_a$ is $G_ab$. Is it contained in $A$? Why?

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    Thank you so much. I got it.2011-06-06