Family of groups with specific presentation
$begingroup$
Is there a name for the family of groups given by $n$ generators ($g_1, g_2,ldots g_n$) and the following relations?
$$g_ig_jg_i = g_jg_ig_j,~forall i,j in lbrace 1,ldots nrbrace,~ineq j\
g_ig_i = 1,forall i in lbrace 1,ldots n rbrace
$$
The relations are quite similar to the ones for a braid group, but then the first relation holds between any pair of generators and the generators are self-inverse.
Is there a name for this family of groups?
group-theory terminology group-presentation combinatorial-group-theory
edited Dec 3 '18 at 1:17
Shaun
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
$endgroup$
add a comment |
$begingroup$
Is there a name for the family of groups given by $n$ generators ($g_1, g_2,ldots g_n$) and the following relations?
$$g_ig_jg_i = g_jg_ig_j,~forall i,j in lbrace 1,ldots nrbrace,~ineq j\
g_ig_i = 1,forall i in lbrace 1,ldots n rbrace
$$
The relations are quite similar to the ones for a braid group, but then the first relation holds between any pair of generators and the generators are self-inverse.
Is there a name for this family of groups?
group-theory terminology group-presentation combinatorial-group-theory
edited Dec 3 '18 at 1:17
Shaun
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
$endgroup$
3
$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38
add a comment |
$begingroup$
Is there a name for the family of groups given by $n$ generators ($g_1, g_2,ldots g_n$) and the following relations?
$$g_ig_jg_i = g_jg_ig_j,~forall i,j in lbrace 1,ldots nrbrace,~ineq j\
g_ig_i = 1,forall i in lbrace 1,ldots n rbrace
$$
The relations are quite similar to the ones for a braid group, but then the first relation holds between any pair of generators and the generators are self-inverse.
Is there a name for this family of groups?
group-theory terminology group-presentation combinatorial-group-theory
edited Dec 3 '18 at 1:17
Shaun
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
$endgroup$
Is there a name for the family of groups given by $n$ generators ($g_1, g_2,ldots g_n$) and the following relations?
$$g_ig_jg_i = g_jg_ig_j,~forall i,j in lbrace 1,ldots nrbrace,~ineq j\
g_ig_i = 1,forall i in lbrace 1,ldots n rbrace
$$
The relations are quite similar to the ones for a braid group, but then the first relation holds between any pair of generators and the generators are self-inverse.
Is there a name for this family of groups?
group-theory terminology group-presentation combinatorial-group-theory
group-theory terminology group-presentation combinatorial-group-theory
edited Dec 3 '18 at 1:17
Shaun
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
edited Dec 3 '18 at 1:17
Shaun
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
edited Dec 3 '18 at 1:17
Shaun
9,246113684
edited Dec 3 '18 at 1:17
Shaun
9,246113684
edited Dec 3 '18 at 1:17
Shaun
9,246113684
9,246113684
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
asked Aug 28 '17 at 9:34
Kenneth GoodenoughKenneth Goodenough
340112
340112
3
$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38
add a comment |
3
$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38
3
3
$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38
$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38
add a comment |
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$begingroup$
You can rewrite this to be the Coxeter group corresponding to the complete Coxeter graph. This will be infinite except in the small trivial cases. I don't think I have seen any special name for it, though someone else might have.
$endgroup$
– Tobias Kildetoft
Aug 28 '17 at 9:38