Timeline for Hopfian property preserved by extensions with finite kernel?

9 events

when toggle format	what		by	license	comment
Dec 18, 2021 at 8:06	history	edited	Martin Sleziak	CC BY-SA 4.0	replaced the link to the arXiv front end; see https://meta.mathoverflow.net/questions/5124/is-it-time-to-replace-links-to-the-ucdavis-arxiv-frontend
Mar 21, 2020 at 16:51	history	edited	YCor	CC BY-SA 4.0	reorganized for the sake of clarity
Dec 3, 2016 at 20:24	comment	added	YCor		@BS. thanks for the correction; this seems to fix the argument.
Jul 22, 2012 at 17:41	comment	added	BS.		On the other hand, a similar idea might work : take $N=F_p[t^2]$ and $M=<N,t^{-1}$. Then $G/N$ is non-Hopfian, but since no non-trivial translation of $\mathbb{Z}$ sends $E={-1,0,2,4,...,2k,...}$ (strictly) inside itself, the conjugation counterexample breaks down and your argument might work.
Jul 22, 2012 at 16:58	comment	added	BS.		Sorry if I missed something, but doesn't conjugation by $diag(t^2,1,1,1)$ define an automorphism of $G$ that sends $M$ strictly inside itself (implying $G/M$ non-Hopfian)?
Jul 22, 2012 at 4:12	history	edited	YCor	CC BY-SA 3.0	Added introducing sentence to make the post more understandable.
Apr 2, 2011 at 23:11	comment	added	Igor Belegradek		I just edited tex by inserting dollar signs etc.
Apr 2, 2011 at 23:10	history	edited	Igor Belegradek	CC BY-SA 2.5	edited tex
Apr 2, 2011 at 21:36	history	answered	YCor	CC BY-SA 2.5