Dear Forum, I am looking for a possibility to transfer relators of one fp group to another free group without transcripting the relators manually. I used in the following example a method, which is very restricting for the variable name of the target free group (= f) and is not allowed in a function, as AssignGeneratorVariables is forbidden there. Is there another possibility?
As an example I reproduced the direct product of symmetric group (3) and alternating group (4). The manual method to produce the mutual relators rel0010 - rel0040 is no problem to me, as this is normally done by automatic methods in my functions. gap> f:=FreeGroup(4);; gap> AssignGeneratorVariables(f); #I Assigned the global variables [ f1, f2, f3, f4 ] gap> s3:=SymmetricGroup(3); Sym( [ 1 .. 3 ] ) gap> a4:=AlternatingGroup(4);; gap> s3fp:=Image(IsomorphismFpGroup(s3));; gap> a4fp:=Image(IsomorphismFpGroup(a4));; gap> prod:=FreeProduct(s3fp,a4fp);; gap> prodrels:=RelatorsOfFpGroup(prod);; gap> rels0010:=[prod.1*prod.3*prod.1^-1*prod.3^-1]; [ f1*f3*f1^-1*f3^-1 ] gap> rels0020:=[prod.1*prod.4*prod.1^-1*prod.4^-1]; [ f1*f4*f1^-1*f4^-1 ] gap> rels0030:=[prod.2*prod.4*prod.2^-1*prod.4^-1]; [ f2*f4*f2^-1*f4^-1 ] gap> rels0040:=[prod.2*prod.3*prod.2^-1*prod.3^-1]; [ f2*f3*f2^-1*f3^-1 ] gap> relscon:=Concatenation(prodrels,rels0010,rels0020,rels0030,rels0040);; gap> relsstr:=String(relscon); "[ f1^2, f2^2, f1*f2*f1*f2*f1*f2, f3^3*f4^-3, f3^3*f4^-1*f3^-1*f4^-1*f3^-1, f3\ ^-1*f4^-1*f3*f4*f3^-1*f4^-1*f3*f4, f1*f3*f1^-1*f3^-1, f1*f4*f1^-1*f4^-1, f2*f4\ *f2^-1*f4^-1, f2*f3*f2^-1*f3^-1 ]" gap> f/EvalString(relsstr); <fp group on the generators [ f1, f2, f3, f4 ]> gap> dirprodfp:=last; <fp group on the generators [ f1, f2, f3, f4 ]> gap> dirprod:=DirectProduct(s3,a4); Group([ (1,2,3), (1,2), (4,5,6), (5,6,7) ]) gap> IsomorphismGroups(dirprodfp,dirprod); [ f1, f2, f3, f4 ] -> [ (1,2), (1,3), (4,7,6), (4,5,6) ] gap> Thank you, Rudolf Zlabinger
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