Orest Xherija
Reputation
580
Top tag
Next privilege 1,000 Rep.
Create tags
 Apr19 comment Abelian group admitting a surjective homomorphism onto an infinite cyclic group I have tried to show that $\ker(g)$ is trivial, but I am failing to do so. My problem is that the $x$ you chose above might have finite order so you would have $nx=0$ with $n \neq 0$ thus the kernel will not be trivial. I cannot find a method to by-pass this problem. Apr17 accepted $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$ Apr16 comment Abelian group admitting a surjective homomorphism onto an infinite cyclic group I am so very sorry for not understanding this immediately. Here is my point of confusion. I cannot see how $G = \ker(f) \times im(g) \implies G \cong \ker(f) \times \Bbb Z$, since $im(g) \subset G$ so you would get $G \cong \ker(f) \times im(g) \subset \ker(f) \times G$ Apr16 asked $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$ Apr16 asked Abelian group admitting a surjective homomorphism onto an infinite cyclic group Apr12 comment Generalised eigenvalue is eigenvalue if it is in the field Thank you very much for your help, Branimir! Apr12 comment Generalised eigenvalue is eigenvalue if it is in the field I see my mistake! Thank you very much for pointing this out! Apr12 accepted Generalised eigenvalue is eigenvalue if it is in the field Apr12 asked Generalised eigenvalue is eigenvalue if it is in the field Mar26 revised Imposing the topology of open rays in $\Bbb R$ deleted 4 characters in body Mar25 revised Imposing the topology of open rays in $\Bbb R$ added 88 characters in body Mar24 comment Imposing the topology of open rays in $\Bbb R$ Dear Brian, I would like to ask your permission to integrate your suggestions and hints into a complete answer in my original post. May I do so? Mar16 revised Imposing the topology of open rays in $\Bbb R$ added 69 characters in body Mar15 comment Imposing the topology of open rays in $\Bbb R$ Thank you very much for your most helpful comments! Mar15 accepted Imposing the topology of open rays in $\Bbb R$ Mar15 asked Imposing the topology of open rays in $\Bbb R$ Mar7 awarded Benefactor Mar4 awarded Nice Question Mar4 awarded Promoter Mar3 awarded Commentator