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Let $S_3$ be the symmetric group on the three objects $x_1, x_2, x_3$.

We are given a (countably infinite) sequence of permutations in $S_3$:

$\sigma_1 \ , \ \sigma_2 \ , \ \sigma_3 \ , \ \ldots \ , \ \sigma_n \ , \ \ldots \ \, .$

Is it true that there exists a positive integer $N$ such that the sequence of products

$\sigma_{N} \ , \ \sigma_{N+1}\sigma_{N} \ , \ \sigma_{N+2}\sigma_{N+1}\sigma_{N} \ , \ldots \, ,$

has a(n infinite) subsequence whose terms fix $x_1$? Thanks!!!

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    I have removed the game theory tag.2011-01-11

1 Answers 1