free product with amalgamation

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wg16
Posts: 2
Joined: Mon Oct 01, 2018 11:29 am

free product with amalgamation

Post by wg16 » Mon Oct 01, 2018 12:00 pm

Hi,
I am a beginner in MAGMA and I've tried to construct a free amalgamated product FPA1 of two groups H1_1 and H2_1 like that:

H1_1:=Group< F1, F2, F3, F4, F5, F6, F7 |
F1^2, F1^-1*F2*F1*F2^-1*F3^-1, F2^2, F1^-1*F3*F1*F3^-2, F2^-1*F3*F2*F3^-2, F3^3, F1^-1*F4*F1*F5^-1*F7^-1*F6^-1, F1^-1*F5*F1*F4^-1*F6^-1, F2^-1*F4*F2*F5^-1*F4^-1*F7^-1*F6^-1,
F2^-1*F5*F2*F5^-1*F7^-1*F6^-1, F3^-1*F4*F3*F5^-1*F4^-1*F6^-1, F3^-1*F5*F3*F4^-1*F6^-1, F4^2*F6^-1, F5^2*F7^-1*F6^-1, F5^-1*F4^-1*F5*F4, F1^-1*F6*F1*F7^-1*F6^-1, F1^-1*F7*F1*F7^-1,
F2^-1*F6*F2*F7^-1, F2^-1*F7*F2*F6^-1, F3^-1*F6*F3*F7^-1, F3^-1*F7*F3*F7^-1*F6^-1, F4^-1*F6*F4*F6^-1, F4^-1*F7*F4*F7^-1, F5^-1*F6*F5*F6^-1, F5^-1*F7*F5*F7^-1, F6^2, F7^2,
F7^-1*F6^-1*F7*F6 >;

H2_1:=Group< F1, F2, F3, F4, F5, F6, F7 |
F1^2*F7^-1, F1^-1*F2*F1*F2^-1*F3^-1*F4^-1, F2^2, F1^-1*F3*F1*F3^-1*F7^-1, F2^-1*F3*F2*F3^-1*F4^-2*F7^-1, F3^2*F4^-1*F7^-1, F1^-1*F4*F1*F4^-1, F2^-1*F4*F2*F4^-2, F3^-1*F4*F3*F4^-1, F4^3,
F1^-1*F5*F1*F5^-1, F1^-1*F6*F1*F6^-1, F2^-1*F5*F2*F5^-1*F7^-1, F2^-1*F6*F2*F6^-1*F5^-1*F7^-1, F3^-1*F5*F3*F6^-1, F3^-1*F6*F3*F6^-1*F5^-1, F4^-1*F5*F4*F6^-1*F5^-1, F4^-1*F6*F4*F5^-1,
F5^2*F7^-1, F6^2*F7^-1, F6^-1*F5^-1*F6*F5*F7^-1, F1^-1*F7*F1*F7^-1, F2^-1*F7*F2*F7^-1, F3^-1*F7*F3*F7^-1, F4^-1*F7*F4*F7^-1, F5^-1*F7*F5*F7^-1, F6^-1*F7*F6*F7^-1, F7^2 >;

FPA1:=Group< fa1, fa2, fa3, fa4, fa5, fa6, fa7, fa8, fa9, fa10, fa11, fa12, fa13, fa14 |
fa1^2, fa1^-1*fa2*fa1*fa2^-1*fa3^-1, fa2^2, fa1^-1*fa3*fa1*fa3^-2, fa2^-1*fa3*fa2*fa3^-2, fa3^3, fa1^-1*fa4*fa1*fa5^-1*fa7^-1*fa6^-1, fa1^-1*fa5*fa1*fa4^-1*fa6^-1,
fa2^-1*fa4*fa2*fa5^-1*fa4^-1*fa7^-1*fa6^-1, fa2^-1*fa5*fa2*fa5^-1*fa7^-1*fa6^-1, fa3^-1*fa4*fa3*fa5^-1*fa4^-1*fa6^-1, fa3^-1*fa5*fa3*fa4^-1*fa6^-1, fa4^2*fa6^-1, fa5^2*fa7^-1*fa6^-1,
fa5^-1*fa4^-1*fa5*fa4, fa1^-1*fa6*fa1*fa7^-1*fa6^-1, fa1^-1*fa7*fa1*fa7^-1, fa2^-1*fa6*fa2*fa7^-1, fa2^-1*fa7*fa2*fa6^-1, fa3^-1*fa6*fa3*fa7^-1, fa3^-1*fa7*fa3*fa7^-1*fa6^-1,
fa4^-1*fa6*fa4*fa6^-1, fa4^-1*fa7*fa4*fa7^-1, fa5^-1*fa6*fa5*fa6^-1, fa5^-1*fa7*fa5*fa7^-1, fa6^2, fa7^2, fa7^-1*fa6^-1*fa7*fa6, fa8^2*fa14^-1, fa8^-1*fa9*fa8*fa9^-1*fa10^-1*fa11^-1,
fa9^2, fa8^-1*fa10*fa8*fa10^-1*fa14^-1, fa9^-1*fa10*fa9*fa10^-1*fa11^-2*fa14^-1, fa10^2*fa11^-1*fa14^-1, fa8^-1*fa11*fa8*fa11^-1, fa9^-1*fa11*fa9*fa11^-2, fa10^-1*fa11*fa10*fa11^-1,
fa11^3, fa8^-1*fa12*fa8*fa12^-1, fa8^-1*fa13*fa8*fa13^-1, fa9^-1*fa12*fa9*fa12^-1*fa14^-1, fa9^-1*fa13*fa9*fa13^-1*fa12^-1*fa14^-1, fa10^-1*fa12*fa10*fa13^-1,
fa10^-1*fa13*fa10*fa13^-1*fa12^-1, fa11^-1*fa12*fa11*fa13^-1*fa12^-1, fa11^-1*fa13*fa11*fa12^-1, fa12^2*fa14^-1, fa13^2*fa14^-1, fa13^-1*fa12^-1*fa13*fa12*fa14^-1,
fa8^-1*fa14*fa8*fa14^-1, fa9^-1*fa14*fa9*fa14^-1, fa10^-1*fa14*fa10*fa14^-1, fa11^-1*fa14*fa11*fa14^-1, fa12^-1*fa14*fa12*fa14^-1, fa13^-1*fa14*fa13*fa14^-1, fa14^2,
fa4*fa5*fa12^-5*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8*fa10*fa9^-1*fa12^-1*fa9*fa10^-1*fa8^2*fa12,
fa6*fa7*fa1*fa12^-5*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8*fa10*fa9^-1*fa12^-1*fa9*fa10^-1*fa8^2*fa12*fa8^-1,
fa6*fa3^2*fa2*fa12^-3*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8^3*fa12^-3*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8*fa10*fa9^-1*fa12^-1*fa9*fa10^-1*fa8^2,
fa6*fa7*fa4*fa5*fa12^-1*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8^3*fa12^-3*fa8^-2*fa10*fa9^-1*fa12*fa8^-1*fa9*fa10^-1*fa8*fa10*fa9^-1*fa12^-1*fa9*fa10^-1*fa8^2*fa12,
fa7*fa5*fa3^2*fa2*fa1*fa12^-2*fa8^-2*fa10*fa9^-1 >;

I need to consider the inclusions of H1_1 and H1_2 into FPA1 and I've tried with

beta_1:=hom< H1_1 -> FPA1 | x :-> x >;


Kernel(beta_1);
^
Runtime error in 'Kernel': Kernel is not computable or representable

but it seems there are some problems. Also, is there a built-in function in MAGMA to compute the free product with amalgamation?

Thank you very much

William

mgates3
Posts: 842
Joined: Fri Jan 06, 2012 2:13 pm

Re: free product with amalgamation

Post by mgates3 » Mon Oct 01, 2018 12:37 pm

You want http://magma.maths.usyd.edu.au/magma/

This forum is for the MAGMA linear algebra library
http://icl.utk.edu/magma/

-mark

wg16
Posts: 2
Joined: Mon Oct 01, 2018 11:29 am

Re: free product with amalgamation

Post by wg16 » Mon Oct 01, 2018 1:18 pm

Ah thank you! Sorry for that.

William

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