mirror of
https://github.com/kalmarek/SmallHyperbolic
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31 lines
3.0 KiB
Plaintext
31 lines
3.0 KiB
Plaintext
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/// Groups with property (T), hyperbolicity unknown
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// H_1
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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)>;
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// H_2
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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)>;
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// H_3
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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)>;
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// H_4
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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>;
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/////////////
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/// Infinite hyperbolic groups, property (T) unknown
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/////////////
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// H_5
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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)>;
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// H_6
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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)>;
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// H_7
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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)>;
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//H_8
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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)>;
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//
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// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ Heisenberg(F₅)
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//
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Hyp1:=Group<a, b, c | a^5, b^5, c^5, comm(a, c), b^-1 * c^-1 * b * c * b * c^-1 * b^-1 * c, b * c^-2 * b * c * b^-2 * c, a * b * a * b^-1 * a^-1 * b * a * b * a^-1 * b^-1 * a^-1 * b * a * b^-1* a^-1 * b^-1, b * a * b * a * b^2 * a^-1 * b * a^2 * b^-2 * a^-1 * b * a^-1 * b^-1 * a^2, b * a^-1 * b * a * b^-1 * a * b^2 * a^-1 * b * a * b^-1 * a * b * a^-1 * b^-1 * a^2, b * a * b^-1 * a * b * a^-1 * b * a^-2 * b^-1 * a^-1 * b * a^-1 * b^-1 * a * b^-1 * a^2, b * a^-1 * b * a^-1 * b^-2 * a * b^-1 * a^-1 * b^-1 * a^-1 * b * a^-2 * b^-2 * a^2, a * b * a^-2 * b^-1 * a^-1 * b^-1 * a^-1 * b^-2 * a * b^-1 * a^-2 * b^2 * a * b^-1, b * a^-2 * b^-1 * a^-2 * b * a * b^-1 * a * b^-1 * a^2 * b^-1 * a * b * a^-2 * b>;
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//
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// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ SL₂(5)
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//
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Hyp2:=Group<a, b, c | a^5, b^5, c^5, comm(a, c), b * c^-1 * b * c * b^-1 * c, b^2 * c^-1 * b^-1 * c^-1 * b^2 * c^-2, a * b * a * b^-1 * a^-1 * b * a * b * a^-1 * b^-1 * a^-1 * b * a * b^-1 * a^-1 * b^-1, b * a * b * a * b^2 * a^-1 * b * a^2 * b^-2 * a^-1 * b * a^-1 * b^-1 * a^2, b * a^-1 * b * a * b^-1 * a * b^2 * a^-1 * b * a * b^-1 * a * b * a^-1 * b^-1 * a^2, b * a * b^-1 * a * b * a^-1 * b * a^-2 * b^-1 * a^-1 * b * a^-1 * b^-1 * a * b^-1 * a^2, b * a^-1 * b * a^-1 * b^-2 * a * b^-1 * a^-1 * b^-1 * a^-1 * b * a^-2 * b^-2 * a^2, a * b * a^-2 * b^-1 * a^-1 * b^-1 * a^-1 * b^-2 * a * b^-1 * a^-2 * b^2 * a * b^-1, b * a^-2 * b^-1 * a^-2 * b * a * b^-1 * a * b^-1 * a^2 * b^-1 * a * b * a^-2 * b>;
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