# Revision history [back]

### How to check if a group given by is finite in SageMath?

Let $G$ be a group generated by

"s1", "s2", "s3", "s4", "s12", "s23", "s34", "s123", "s234", "s1234"


with relations

s1^2, s2^2, s3^2, s4^2, s12^2, s23^2, s34^2, s123^2, s234^2, s1234^2, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, s1*s3*s1*s3, s2*s4*s2*s4, s1*s4*s1*s4,s1*s12*s2*s12, s4*s34*s3*s34, s3*s123*s23*s12*s3*s123*s23*s12, s123*s12*s4*s34*s4*s12*s2, s23*s1234*s12*s3*s4*s3*s12,s23*s1234*s34*s1*s2*s1*s34


All the above equal to the identity $e$ of $G$.

Is there some function in SageMath which could check if $G$ is finite or not? Thank you very much.

### How to check if a group given by is finite in SageMath?

Let $G$ be a group generated by

"s1", "s2", "s3", "s4", "s12", "s23", "s34", "s123", "s234", "s1234"


with relations

s1^2, s2^2, s3^2, s4^2, s12^2, s23^2, s34^2, s123^2, s234^2, s1234^2, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, s1*s3*s1*s3, s2*s4*s2*s4, s1*s4*s1*s4,s1*s12*s2*s12, s4*s34*s3*s34, s3*s123*s23*s12*s3*s123*s23*s12, s123*s12*s4*s34*s4*s12*s2, s23*s1234*s12*s3*s4*s3*s12,s23*s1234*s34*s1*s2*s1*s34


All the above equal to the identity $e$ of $G$.

Is there some function in SageMath which could check if $G$ is finite or not? Thank you very much.

 3 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### How to check if a group given by is finite in SageMath?

Let $G$ be a group generated by

"s1", "s2", "s3", "s4", "s12", "s23", "s34", "s123", "s234", "s1234"


with relations

s1^2, s2^2, s3^2, s4^2, s12^2, s23^2, s34^2, s123^2, s234^2, s1234^2, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, s1*s3*s1*s3, s2*s4*s2*s4, s1*s4*s1*s4,s1*s12*s2*s12, s4*s34*s3*s34, s3*s123*s23*s12*s3*s123*s23*s12, s123*s12*s4*s34*s4*s12*s2, s23*s1234*s12*s3*s4*s3*s12,s23*s1234*s34*s1*s2*s1*s34


All the above equal to the identity $e$ of $G$.

Is there some function in SageMath which could check if $G$ is finite or not? Thank you very much.

 4 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### How to check if a group given by a presentation is finite in SageMath?

Let $G$ be a group generated by

"s1", "s2", "s3", "s4", "s12", "s23", "s34", "s123", "s234", "s1234"


with relations

s1^2, s2^2, s3^2, s4^2, s12^2, s23^2, s34^2, s123^2, s234^2, s1234^2, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, s1*s3*s1*s3, s2*s4*s2*s4, s1*s4*s1*s4,s1*s12*s2*s12, s4*s34*s3*s34, s3*s123*s23*s12*s3*s123*s23*s12, s123*s12*s4*s34*s4*s12*s2, s23*s1234*s12*s3*s4*s3*s12,s23*s1234*s34*s1*s2*s1*s34


All the above equal to the identity $e$ of $G$.

Is there some function in SageMath which could check if $G$ is finite or not? Thank you very much.

 5 None dan_fulea 5397 ●5 ●43 ●91

### How to check if Finiteness of a group given by a presentation is finite in SageMath?presentation

Let $G$ be a group generated by

"s1", "s2", "s3", "s4", "s12", "s23", "s34", "s123", "s234", "s1234"


with relations

[ s1^2, s2^2, s3^2, s4^2, s4^2,
s12^2, s23^2, s34^2, s34^2,
s123^2, s234^2, s1234^2, s234^2,
s1234^2,
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, s3*s4*s3*s4*s3*s4,
s1*s3*s1*s3, s2*s4*s2*s4, s1*s4*s1*s4,s1*s12*s2*s12, s4*s34*s3*s34, s3*s123*s23*s12*s3*s123*s23*s12, s123*s12*s4*s34*s4*s12*s2, s23*s1234*s12*s3*s4*s3*s12,s23*s1234*s34*s1*s2*s1*s34
s1*s4*s1*s4,
s1*s12*s2*s12,
s4*s34*s3*s34,
s3*s123*s23*s12*s3*s123*s23*s12,
s123*s12*s4*s34*s4*s12*s2,
s23*s1234*s12*s3*s4*s3*s12,
s23*s1234*s34*s1*s2*s1*s34 ]

# s1       s2       s3       s4
# o--------o--------o--------o
#
#    non-standard joining relations
#
#     s12      s23       s34
#     o        o         o
#
#    non-standard joining relations
#
#         s123     s234
#         o        o
#
#    non-standard joining relations
#
#             s1234
#             o


All the above equal to the identity $e$ of $G$.

Is there some function in SageMath which could check if $G$ is finite or not? Thank you very much.