Conjugacy in right-angled Artin groups
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
asked 6 hours ago
AGenevois
1,190613
add a comment |
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
asked 6 hours ago
AGenevois
1,190613
add a comment |
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
asked 6 hours ago
AGenevois
1,190613
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
asked 6 hours ago
AGenevois
1,190613
asked 6 hours ago
AGenevois
1,190613
asked 6 hours ago
AGenevois
1,190613
asked 6 hours ago
AGenevois
1,190613
asked 6 hours ago
AGenevois
1,190613
1,190613
add a comment |
add a comment |
1 Answer
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Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.
answered 5 hours ago
Benjamin Steinberg
22.9k265124
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.
answered 5 hours ago
Benjamin Steinberg
22.9k265124
add a comment |
Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.
answered 5 hours ago
Benjamin Steinberg
22.9k265124
add a comment |
Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.
answered 5 hours ago
Benjamin Steinberg
22.9k265124
Look at Lemma 9 of https://arxiv.org/abs/0802.1771 for what you want.
answered 5 hours ago
Benjamin Steinberg
22.9k265124
answered 5 hours ago
Benjamin Steinberg
22.9k265124
answered 5 hours ago
Benjamin Steinberg
22.9k265124
answered 5 hours ago
Benjamin Steinberg
22.9k265124
22.9k265124
add a comment |
add a comment |
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