[GAP Forum] finding automorphisms of finitely presented groups

[Alexander Hulpke]

Dear GAP-Forum,

On Mar 16, 2006, at 5:58 AM, Robert Heffernan wrote:

> I do have a followup question, if anybody can help.
> I have created a finitely presented group G
> F:=FreeGroup("a","b","c","d");;a:=F.1;;b:=F.2;;c:=F.3;;d:=F. 
> 4;;rels:= <some words in terms of a,b,c and d>G:=F/rels;a:=G. 
> 1;;b:=G.2;;c:=G.3;;d:=G.4;;
> I have then created a new set of words/relations, rels2 say, in  
> termsof a,b,c and d (by calculating with things in G).
> Now I want to create a new finitely presented group in a manner  
> such as this:H:=F/rels2;
> However, I can't do this directly as a,b,c and d are now elements  
> of G, not F.
> I can't find a simple way to relate a,b,c and d back to the  
> generatorsof the free group F,

You have three options. In order from ``cleanest'' to ``most  
technical'':
a) From a `GroupHomomorphismByImages' from F to G, mapping F.i to  
G.i. Then take the `PreImagesRepresentative' of your words.
b) Use `MappedWord' to map a word in the G.i to a word in the F.i
c) For any element of G, `UnderlyingElement' returns the  
corresponding element of F, i.e. the relators you want.

Best wishes,

     Alexander Hulpke


-- Colorado State University, Department of Mathematics,
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