Conjugacy in right-angled Artin groups












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I am looking for a reference containing the following result:




Let $a$ and $b$ be two elements of a right-angled Artin group $A$. Assume that $a$ and $b$ have minimal length (with respect to the canonical generating set of $A$) in their conjugacy classes. Let $a_1 cdots a_n$ and $b_1 cdots b_m$ be words of minimal length representing $a$ and $b$ respectively. If $a$ and $b$ are conjugate in $A$, then $a_1 cdots a_n$ can be obtained from $b_1 cdots b_m$ by applying the following operations: permutation of two successive letters which commute, and cyclic permutation.




I am sure that it is written somewhere, but I am not able to find where.






reference-request gr.group-theory combinatorial-group-theory







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    I am looking for a reference containing the following result:




    Let $a$ and $b$ be two elements of a right-angled Artin group $A$. Assume that $a$ and $b$ have minimal length (with respect to the canonical generating set of $A$) in their conjugacy classes. Let $a_1 cdots a_n$ and $b_1 cdots b_m$ be words of minimal length representing $a$ and $b$ respectively. If $a$ and $b$ are conjugate in $A$, then $a_1 cdots a_n$ can be obtained from $b_1 cdots b_m$ by applying the following operations: permutation of two successive letters which commute, and cyclic permutation.




    I am sure that it is written somewhere, but I am not able to find where.






    reference-request gr.group-theory combinatorial-group-theory







    share|cite|improve this question

























      2












      2








      2


      1





      I am looking for a reference containing the following result:




      Let $a$ and $b$ be two elements of a right-angled Artin group $A$. Assume that $a$ and $b$ have minimal length (with respect to the canonical generating set of $A$) in their conjugacy classes. Let $a_1 cdots a_n$ and $b_1 cdots b_m$ be words of minimal length representing $a$ and $b$ respectively. If $a$ and $b$ are conjugate in $A$, then $a_1 cdots a_n$ can be obtained from $b_1 cdots b_m$ by applying the following operations: permutation of two successive letters which commute, and cyclic permutation.




      I am sure that it is written somewhere, but I am not able to find where.






      reference-request gr.group-theory combinatorial-group-theory







      share|cite|improve this question













      I am looking for a reference containing the following result:




      Let $a$ and $b$ be two elements of a right-angled Artin group $A$. Assume that $a$ and $b$ have minimal length (with respect to the canonical generating set of $A$) in their conjugacy classes. Let $a_1 cdots a_n$ and $b_1 cdots b_m$ be words of minimal length representing $a$ and $b$ respectively. If $a$ and $b$ are conjugate in $A$, then $a_1 cdots a_n$ can be obtained from $b_1 cdots b_m$ by applying the following operations: permutation of two successive letters which commute, and cyclic permutation.




      I am sure that it is written somewhere, but I am not able to find where.






      reference-request gr.group-theory combinatorial-group-theory




      reference-request gr.group-theory combinatorial-group-theory






      share|cite|improve this question













      share|cite|improve this question











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      asked 4 hours ago









      AGenevois

      1,190612




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          Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.






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            1 Answer
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            1 Answer
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            active

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            Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.






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              2














              Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.






              share|cite|improve this answer
























                2












                2








                2






                Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.






                share|cite|improve this answer












                Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.







                share|cite|improve this answer












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                answered 3 hours ago









                Benjamin Steinberg

                22.9k265124




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