[GAP Forum] a multiplicative group generated by an indeterminate

[Alexander Hulpke]

Dear Forum, Dear Igor Korepanov,

> suppose  a  is an indeterminate over rationals and I want to create a group consisting of this  a  raised to all integer powers:
> 
> 
> gap> a := Indeterminate( Rationals,"a" );
> a
> gap> g := Group( a );
> #I  default `IsGeneratorsOfMagmaWithInverses' method returns `true' for [ a ]
> <group with 1 generators>
> gap> 
> 
> 
> Now the question: does this mean that I should better do it another way? Or proceed bravely?

The warning here is harmless -- it just means that GAP has not been told that this set will fulfill the group axioms and is cautious.
However you will find very little (if any) functionality for the resulting group and will probably find it easier to work in the isomorphic
FreeGroup(1)

> 
> Also, is there a way to define the group of all nonzero rationals other than  GL(1,Rationals)  ?
This will not work, nor am I aware of any other method. A fundamental issue with it is that this is not a finitely generated group.

Best,

   Alexander Hulpke




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