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domotorp
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Boris Novikov
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I'm working on some palindromic words right now. Those are the elements of F_2$F_2$, the free group on two generators, which are the same if reveresed. For example $xyx, y^2, xyxxyx$ and so on.

Can you write each element of F'$F'$, the derived group, as a product of palindromes of EVEN length? Does this property hold if you are not in F$F$, but in a group G$G$ in which you know that every element is a product of at most n$n$ palindromes? If G$G$ has this property then G$G$ has finite palindromic width.

I've puzzled around quite a bit but can't find a way of even writing $x^{-1}y^{-1}xy$ as a product of palindromes of even length.

Thanks, Elisabeth

I'm working on some palindromic words right now. Those are the elements of F_2, the free group on two generators, which are the same if reveresed. For example $xyx, y^2, xyxxyx$ and so on.

Can you write each element of F', the derived group, as a product of palindromes of EVEN length? Does this property hold if you are not in F, but in a group G in which you know that every element is a product of at most n palindromes? If G has this property then G has finite palindromic width.

I've puzzled around quite a bit but can't find a way of even writing $x^{-1}y^{-1}xy$ as a product of palindromes of even length.

Thanks, Elisabeth

I'm working on some palindromic words right now. Those are the elements of $F_2$, the free group on two generators, which are the same if reveresed. For example $xyx, y^2, xyxxyx$ and so on.

Can you write each element of $F'$, the derived group, as a product of palindromes of EVEN length? Does this property hold if you are not in $F$, but in a group $G$ in which you know that every element is a product of at most $n$ palindromes? If $G$ has this property then $G$ has finite palindromic width.

I've puzzled around quite a bit but can't find a way of even writing $x^{-1}y^{-1}xy$ as a product of palindromes of even length.

Thanks, Elisabeth

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Elisabeth Fink
Elisabeth Fink
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$\left[x,y\right]$ as a product of palindromes of even length?

I'm working on some palindromic words right now. Those are the elements of F_2, the free group on two generators, which are the same if reveresed. For example $xyx, y^2, xyxxyx$ and so on.

Can you write each element of F', the derived group, as a product of palindromes of EVEN length? Does this property hold if you are not in F, but in a group G in which you know that every element is a product of at most n palindromes? If G has this property then G has finite palindromic width.

I've puzzled around quite a bit but can't find a way of even writing $x^{-1}y^{-1}xy$ as a product of palindromes of even length.

Thanks, Elisabeth