Talk:Nielsen transformation
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Ordered Sets (and the Word Problem)
[edit]I have changed the sets into ordered sets. The Neilsen transformation does not make sense in an unordered set, as .
![{\displaystyle [x_{1},\ldots ,x_{n}]\mapsto [x_{2},\ldots ,x_{n},x_{1}]}](https://wikimedia.riteme.site/api/rest_v1/media/math/render/svg/f855aa6c608de44e63cb91b9010b68731ccf5379)
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
[edit]
The footnote to the page states that in a finite -generated group, all generating sets of size are equivalent. Is this really true? It does not seem obvious. What is obvious is that any two generating sets of size are equivalent as generating sets of size (extending by the trivial element). Sean Eberhard (talk) 12:42, 26 June 2023 (UTC)
