- #1
Euge
Gold Member
MHB
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Here's this week's problem!
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Problem. Show that the short exact sequence of abelian groups
\(\displaystyle 0 \rightarrow \bigoplus_p \Bbb Z/(p) \rightarrow \prod_p \Bbb Z/(p) \rightarrow \frac{\prod_p \Bbb Z/(p)}{\bigoplus_p \Bbb Z /(p)} \rightarrow 0\)
is not split exact. (The sums and products are extended over all prime numbers $p$.)
_____________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Problem. Show that the short exact sequence of abelian groups
\(\displaystyle 0 \rightarrow \bigoplus_p \Bbb Z/(p) \rightarrow \prod_p \Bbb Z/(p) \rightarrow \frac{\prod_p \Bbb Z/(p)}{\bigoplus_p \Bbb Z /(p)} \rightarrow 0\)
is not split exact. (The sums and products are extended over all prime numbers $p$.)
_____________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!