Let $0\to A\xrightarrow{f} A\oplus B\xrightarrow{g}B\to 0$ be a short exact sequence of (finite) abelian groups, then must it be split exact? If not, can you show me some examples? Thanks!
Asked
Active
Viewed 89 times
2
-
Thanks @DanielRobert-Nicoud – LipCaty Sep 22 '17 at 13:38
-
If I emphisize that A and B are finite abelian groups, is it split? – LipCaty Sep 22 '17 at 13:41
-
Yes, see https://math.stackexchange.com/a/891527/60713 – Daniel Robert-Nicoud Sep 22 '17 at 14:00