Talk:Goursat's lemma

Copied from Lang?

The second paragraph of this article appears to be copied from exercise I.5 of Lang's Algebra, with "Show that" changed to "Then". This text was introduced (using "And then" instead of "Then") in this diff. (Strangely, the original version is a solution of exercise I.6...) Michael Slone (talk) 09:01, 31 December 2007 (UTC)

It also appears in a variety (pun not intended) of papers as well as in Bourbaki's Algebra I.

I'd be willing to bet that's where Lang picked it up, although he was a member, so he may have contributed to that volume ;)

Mavros-Belas (talk) 21:52, 7 January 2008 (UTC)Mavros-Belas

I've added a more in-depth reference on this (Lambek). I can't find "Goursat" mentioned in Bourbaki 1-3, so what is it called there? Actually, I can't even find Maltsev (even spelled as Mal'cev) varieties in Bourbaki... (And by this I mean discussed as a variety.) Their coverage of universal algebra isn't great. 86.127.138.67 (talk) 02:20, 18 April 2015 (UTC)

Surjectivity Condition Needed

Pg 25 of Alperin and Bell's in q8, the surjectivity condition that the subgroup is a subdirect product is dropped. There is an equivalent statement that any subgroup in the tuple has a bijection to two piecewise isomorphic sections having a unique isomorphism. Can anyone clarify this? — Preceding unsigned comment added by 2405:205:4292:93C5:61B8:7AC9:83B:8F22 (talk) 13:26, 12 February 2018 (UTC)

3-permutability

Is being a Goursat variety the same as 3-permutability of congruences? -- Walt Pohl (talk) 07:28, 14 April 2020 (UTC)