mirror of
https://github.com/kalmarek/SmallHyperbolic
synced 2024-10-06 13:05:36 +02:00
23 lines
1.5 KiB
Plaintext
23 lines
1.5 KiB
Plaintext
/////////////
|
|
/// Groups with property (T), hyperbolicity unknown
|
|
/////////////
|
|
// H_1
|
|
H_1:=Group<a, b, c |a^5, b^5, c^5, comm(a, b, a), comm(a, b, b), comm(b,c,b),comm(b,c,c), comm(a,c,a), comm(a,c,c)>;
|
|
// H_2
|
|
H_2:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, comm(b,c,b),comm(b,c,c), comm(a,c,a),comm(a,c,c)>;
|
|
// H_3
|
|
H_3:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, comm(a,c,a),comm(a,c,c)>;
|
|
// H_4
|
|
H_4:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, a^-1 * c * a * c^-1 * a * c, c^-2 * a * c * a * c^-2 * a^2>;
|
|
/////////////
|
|
/// Infinite hyperbolic groups, property (T) unknown
|
|
/////////////
|
|
// H_5
|
|
H_5:=Group<a, b, c |a^5, b^5, c^5, comm(a, b, a), comm(a, b, b), comm(b,c,b),comm(b,c,c), comm(a,c,a),comm(a,c,c,a),comm(a,c,c,c)>;
|
|
// H_6
|
|
H_6:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, comm(b,c,b),comm(b,c,c), comm(a,c,a),comm(a,c,c,a),comm(a,c,c,c)>;
|
|
// H_7
|
|
H_7:=Group<a, b, c |a^5, b^5, c^5, comm(a, b, a), comm(a, b, b), b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, comm(a,c,a), comm(a,c,c,a), comm(a,c,c,c)>;
|
|
//H_8
|
|
H_8:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, comm(a,c,a), comm(a,c,c,a), comm(a,c,c,c)>;
|