# Finiteness of a group given by a 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,
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 ]
# 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.

`G.is_finite()`

?