-3

Do you know a reference which contains a proof for this proposition:

A set containing an element $a$, allows an Abelian group structure with identity element $a$.

?

By reference, I mean a formal reference to a paper or a book.

Minimus Heximus
  • 1,512

1 Answers1

2

The answer by Asaf Karagila at

this stack exchange posting

is rather thorough, and shows that the claim isn't necessarily true unless you believe the Axiom of Choice. I found it by looking at the list of "Related" questions to the right of your question. :)

Remark: I've now been downvoted for this answer. If this isn't a "reference" with a "proof," then I don't know what is. If OP meant "published in a printed-on-paper journal", perhaps OP should have said so.

Community
  • 1
John Hughes
  • 93,729
  • I have the proof, but I need a reference to a paper or a book instead. – Minimus Heximus Jun 06 '15 at 11:05
  • 2
  • You should have said so. 2. Is there someone that requires this? Perhaps you could provide the URL citation, and then include the body of Asaf's answer as an appendix if your editor/advisor/whatever doesn't want to allow it. I'll bet Asaf would be willing to give you the right to do so.
    • – John Hughes Jun 06 '15 at 11:08
  • Yes. I forgot 'reference' has a more general meaning in English. I added this to the question. – Minimus Heximus Jun 06 '15 at 11:09
  • and yes a journal editor has requested to add a reference for this. But it is a personal matter and mentioning this is not appropriate for the question. – Minimus Heximus Jun 06 '15 at 11:13