Talk:Nielsen transformation

Ordered Sets (and the Word Problem)

I have changed the sets into ordered sets. The Neilsen transformation $[x_{1},\ldots ,x_{n}]\mapsto [x_{2},\ldots ,x_{n},x_{1}]$ does not make sense in an unordered set, as $\{x_{1},\ldots ,x_{n}\}=\{x_{2},\ldots ,x_{n},x_{1}\}$.

Also, I am sceptical about the section entitled "word problem". Surely this section is discussing the isomorphism problem?!? —Preceding unsigned comment added by 130.209.6.40 (talk) 12:51, 4 May 2010 (UTC)

Generating sets of size $d+1$

The footnote to the page states that in a finite $d$-generated group, all generating sets of size $d+1$ are equivalent. Is this really true? It does not seem obvious. What is obvious is that any two generating sets of size $d$ are equivalent as generating sets of size $d+1$ (extending by the trivial element). Sean Eberhard (talk) 12:42, 26 June 2023 (UTC)