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add two 555 examples

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kalmarek 2020-04-23 16:45:32 +02:00
parent bc183ec5f4
commit 12d0bd897f
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2 changed files with 9 additions and 2 deletions
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3
Makefile
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@ -8,8 +8,7 @@ GROUPS344 = 14_40_40_0 14_40_48_0 14_40_54_0 14_40_54_2 14_48_48_0 14_48_48_1 14
GROUPS444 = 40_40_40_0 40_40_48_0 40_40_54_0 40_48_48_0 40_48_54_0 40_48_54_2 40_54_54_0 40_54_54_2 40_54_54_8 48_48_48_0 48_48_48_1 48_48_54_0 48_54_54_0 48_54_54_2 48_54_54_8 54_54_54_0 54_54_54_2
GROUPS555 = H_1 H_2 H_3 H_4 H_5 H_6 H_7 H_8
GROUPS555 = H_1 H_2 H_3 H_4 H_5 H_6 H_7 H_8 Hyp1 Hyp2
JULIA = /opt/bin/julia

8
data/presentations_5_5_5.txt
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@ -20,3 +20,11 @@ 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
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)>;
//
// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ Heisenberg(F₅)
//
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>;
//
// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ SL₂(5)
//
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>;