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Ketan Patel
Ketan Patel
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How to find finite subgroupsquotients of infinite triangle groups or von Dyck groups?

Hi all,

I need the following information about the subgroupquotients of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic ($1/l+1/m+1/n<1$) triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groupsgiven quotients of this group is finite?

(2) Is there exist any reference where such quotient groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

How to find finite subgroups of infinite triangle groups or von Dyck groups?

Hi all,

I need the following information about the subgroup of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic ($1/l+1/m+1/n<1$) triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groups is finite?

(2) Is there exist any reference where such groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

How to find quotients of infinite triangle groups or von Dyck groups?

I need the following information about the quotients of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic ($1/l+1/m+1/n<1$) triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the given quotients of this group is finite?

(2) Is there exist any reference where such quotient groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

added 18 characters in body
Source Link
Ketan Patel
Ketan Patel
  • 21
  • 2

Hi all,

I need the following information about the subgroup of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic ($1/l+1/m+1/n<1$) triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groups is finite?

(2) Is there exist any reference where such groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

Hi all,

I need the following information about the subgroup of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groups is finite?

(2) Is there exist any reference where such groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

Hi all,

I need the following information about the subgroup of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic ($1/l+1/m+1/n<1$) triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groups is finite?

(2) Is there exist any reference where such groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel

Source Link
Ketan Patel
Ketan Patel
  • 21
  • 2

How to find finite subgroups of infinite triangle groups or von Dyck groups?

Hi all,

I need the following information about the subgroup of infinite triangle (or von Dyck) groups.

(1) Let $G(l,m,n)$ defined as $S^l$ =$T^m$ = $(ST)^n$ = $E$ is the hyperbolic triangle group. What are the additional conditions $S$ and $T$ should satisfy in order to ensure that the groups is finite?

(2) Is there exist any reference where such groups have been identified as isomorphic to other famous group?

I am a student of Physics and have very limited knowledge of the group theory, so simple answer will be very helpful.

Thanks in advance.

Ketan Patel