Timeline for Recognize this countably generated abelian group?

10 events

when toggle format	what		by	license	comment
Oct 30, 2015 at 20:37	vote	accept	Aeryk
Oct 30, 2015 at 20:37	history	edited	Aeryk	CC BY-SA 3.0	Fixed isomorphism according to discussion in comments
Oct 30, 2015 at 20:31	comment	added	Aeryk		@JulianRosen: Egads, you're right! I was computing my factor group incorrectly. Instead of modding out by $<g_k>$, I was effectively modding out by $<g_k, g_{k+1}, \dots>$. I'll correct that above. Thanks!
Oct 30, 2015 at 19:57	comment	added	Julian Rosen		If you believe my answer, then $G_{(p,q)}/\langle g_k\rangle \cong \mathbb{Z}[1/q]/\langle p^k/q^k \rangle$ is an infinite group, so cannot be $\mathbb{Z}/p^k\mathbb{Z}$.
Oct 30, 2015 at 19:29	history	edited	Aeryk	CC BY-SA 3.0	Added more info about the group and the reasons behing the restrictions on p and q.
Oct 30, 2015 at 19:29	answer	added	Julian Rosen		timeline score: 10
Oct 30, 2015 at 19:18	comment	added	Aeryk		@AnthonyQuas: I thought something similar, but wouldn't $p$-adic integers with finite expansions (and a $+$ or $-$ sign) just be regular integers?
Oct 30, 2015 at 19:07	comment	added	Anthony Quas		I think this is the subgroup of $p$-adic integers consisting of those $p$-adic integers with finite expansions.
Oct 30, 2015 at 19:01	history	edited	Aeryk	CC BY-SA 3.0	edited body
Oct 30, 2015 at 18:50	history	asked	Aeryk	CC BY-SA 3.0