[GAP Forum] Inequality of Generators of Finitely Presented and corresponding Free Group

[Gaurav Dhingra]

Hi, GAP forum members

I am reading this particular documentation 
http://www.gap-system.org/Manuals/doc/ref/chap47.html , from this page i 
quote this sentence

 > That means that words in the generators of the free group are not 
elements of the finitely presented group. Vice versa elements of the 
FpGroup are not words.

There is also an example showing this behavior. Now, i don't why this 
has been done. I mean is there is any particular reason for why GAP 
authors did it this way? (for defining equality between the generators).
Feel free explain in detail even if it is completely some development 
methodology (or non-mathematical) which has been followed for this.

Thanks
Gaurav Dhingra