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Aug 23, 2012 at 16:10 comment added Alexander Shamov I don't understand the question now. What is this $S$ for? And I believe that my counterexample applies here for trivial reasons: if there is no transformation at all, then surely there is no transformation in $S$, right? And by the way, if you place $'s around your LaTeX code, it would be easier to read.
Aug 23, 2012 at 10:43 comment added bogdan Thabk you! I will update the question.
Aug 22, 2012 at 20:18 history answered Alexander Shamov CC BY-SA 3.0