[GAP Forum] Van Kampen theoriem for the Klein bottle applied to fp groups

[Alexander Hulpke]

Dear Forum,

Marc Bogaerts asked:

> So initially I thought I was wrong but when frolicking around with these
> two relators I found the following:
> a*b *a^-1*b = 1 implies a*b*a^-2a*b. So if I put u:=a*b and v :=a then the
> last equation becomes
> u*v^-2*u = 1 or u^2*v^-2, so the two presentations are equivalent.
> I found this relationship totally by good luck, but I wonder if there could
> have been a way
> using Gap to establish an isomorphism between those two groups?

Beyond the trivial (using guided Tietze transformations where you supply the rewriting) there is no method in GAP that would automatically find such an isomorphism. 

The paper 
Holt, D.F.; Rees, Sarah
Testing for isomorphism between finitely presented groups. (English)
Liebeck, Martin (ed.) et al., Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, held July 5-15, 1990 in Durham, UK. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 165, 459-475 (1992).

describes such an algorithm which has been implemented in a system `QUOTPIC', but it is not available in GAP. I am not sure about current availability of an implementation.

Best,

  Alexander Hulpke