Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

let $G$ be an abelian group. and $f:G\rightarrow \{0\}$ be the trivial homomorphism. suppose there exists $G\stackrel{g}{\rightarrow} H \stackrel{h}{\rightarrow} \{0\}$ such that $f=h\circ g$ does this imply that necessarely $H=\{0\}$ if not then under what condition this is true?

share|improve this question
3  
I noticed that you've asked 7 questions, all of which have been answered, but you haven't accepted any answers, nor have you even clicked on an "up arrow" to vote for an answer. People here are putting time in to addressing your questions; you should at least vote for answers that are helpful, and accept at least some of the answers offered. –  amWhy May 31 '11 at 1:56

1 Answer 1

up vote 1 down vote accepted

No, it does not. Take $H=G$, $g=id$, and $h$ the trivial homomorphism.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.