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)