I am reading Dummit and Foote's book: Abstract Algebra ... ... and am currently focused on Section 6.3 A Word on Free Groups ...(adsbygoogle = window.adsbygoogle || []).push({});

I have a basic question regarding the nature and character of free groups ...

Dummit and Foote's introduction to free groups reads as follows:

In the above text, Dummit and Foote write the following:

" ... ... The basic idea of a free group ##F(S)## generated by a set ##S## is that there are no satisfied by any of the elements in ##S## (##S## is "free"of relations.) ... ... "

Dummit and Foote then show how to construct ##F(S)## as the set of all words (together with inverses) ... but they do not seem to prove that given that ##F(S)## contains all words in ##S## there are no relations satisfied by any of the elements in ##S## ... ...

Is the lack of a rigorous proof because the lack of any such relations is obvious ... ?

Can someone please help clarify this situation ...?

Peter

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# I Free Groups - Dmmit & Fooote - Section 6.3

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