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Apr 11, 2017 at 20:54 vote accept user148212
Apr 11, 2017 at 20:26 comment added Jay Taylor The point here is that $x$ is unique up to right multiplication by elements of $T_0$.
Apr 11, 2017 at 20:26 history edited Jay Taylor CC BY-SA 3.0
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Apr 11, 2017 at 19:54 comment added Jay Taylor Yes, one can already see this from the first part of the answer. I'll update the answer to make it clearer.
Apr 11, 2017 at 15:53 comment added user148212 Thank you. Does this property actually only depends on $T$, i.e. is it possible that there are $x$ and $y$ such that ${^xT_0}={^yT_0}$ but $x^{-1}F(x)$ represents an element in the centraliser while $y^{-1}F(y)$ does not?
Apr 11, 2017 at 13:55 history edited Jay Taylor CC BY-SA 3.0
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Apr 11, 2017 at 13:33 history answered Jay Taylor CC BY-SA 3.0