Given a presentation of a group, find its normalizer.
Let $F$ and $H$ be two free groups, where $F = langle a,brangle$ and $H = langle aa,bb,aba,baab, bababrangle$. Let $N(H)$ be the normalizer of $H$ in $F$.
How can I compute $N(H)/H$?
In general, given a presentation of a group, is there a way to find its normalizer?
group-theory free-groups group-presentation combinatorial-group-theory
edited Nov 30 at 1:56
Shaun
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
add a comment |
Let $F$ and $H$ be two free groups, where $F = langle a,brangle$ and $H = langle aa,bb,aba,baab, bababrangle$. Let $N(H)$ be the normalizer of $H$ in $F$.
How can I compute $N(H)/H$?
In general, given a presentation of a group, is there a way to find its normalizer?
group-theory free-groups group-presentation combinatorial-group-theory
edited Nov 30 at 1:56
Shaun
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
2
In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18
add a comment |
Let $F$ and $H$ be two free groups, where $F = langle a,brangle$ and $H = langle aa,bb,aba,baab, bababrangle$. Let $N(H)$ be the normalizer of $H$ in $F$.
How can I compute $N(H)/H$?
In general, given a presentation of a group, is there a way to find its normalizer?
group-theory free-groups group-presentation combinatorial-group-theory
edited Nov 30 at 1:56
Shaun
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
Let $F$ and $H$ be two free groups, where $F = langle a,brangle$ and $H = langle aa,bb,aba,baab, bababrangle$. Let $N(H)$ be the normalizer of $H$ in $F$.
How can I compute $N(H)/H$?
In general, given a presentation of a group, is there a way to find its normalizer?
group-theory free-groups group-presentation combinatorial-group-theory
group-theory free-groups group-presentation combinatorial-group-theory
edited Nov 30 at 1:56
Shaun
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
edited Nov 30 at 1:56
Shaun
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
edited Nov 30 at 1:56
Shaun
8,507113580
edited Nov 30 at 1:56
Shaun
8,507113580
edited Nov 30 at 1:56
Shaun
8,507113580
8,507113580
asked Apr 29 '17 at 5:04
Yuliya
132
asked Apr 29 '17 at 5:04
Yuliya
132
asked Apr 29 '17 at 5:04
Yuliya
132
132
2
In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18
add a comment |
2
In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18
2
2
In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18
In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18
add a comment |
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In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite.
– Derek Holt
Apr 29 '17 at 8:18