Talk:Trivial group

Smallest Field

Isn't this also the smallest feild?

No, a field (mathematics) must have a distinct 0 and 1, so Z₂ is the smallest field.--agr 21:54, 7 September 2006 (UTC)

For $F$ to be a field, $F-\{0\}$ should be a group under multiplication; since the empty set is never a group, this is not true for $\mathbb {Z} _{1}$. --Ian Maxwell 19:57, 21 April 2007 (UTC)

No Trivial Field Exists

We should consider adding the fact that no trivial field exists (0=1) to the main article because it adds more appreciation for the trivial group. — Preceding unsigned comment added by 99.149.190.128 (talk) 22:43, 22 August 2012 (UTC)

This comment may be appropriate with the article Trivial ring, which has a similar structure to a field. This has already been highlighted in that article, though I so not feel that what it illustrates relates to "specialness" of trivial rings or groups, but to the convolutedness of the definition of a field. The non-existence of the field with one element is rather akin to the number 1 being excluded as a prime number. It would be inappropriate to mention fields in this article. — Quondum^☏ 10:05, 23 August 2012 (UTC)