Timeline for Lifting of algebraic fibrations via a subnormal series

6 events

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Jan 17 at 15:09	comment	added	Matt Zaremsky		When you say "lift" do you mean you want the restriction of $\varphi'$ to $G_1$ to equal $\varphi$? Or do you just want $G$ to fiber, period? Either way I think there's not a good way to ensure this, for example it's easy to find groups with finite abelianization that have finite index subgroups that fiber (e.g., various right-angled Coxeter groups). So even in the "very nice" case when $n=1$ and $G/G_1$ is finite this doesn't need to happen.
Jan 17 at 12:50	comment	added	Marcos		@DaveBenson Nice example. But what about ''easy groups''? Maybe we can add some reasonable property to $G$ that avoids weird behaviours.
Jan 17 at 12:28	comment	added	Dave Benson		Consider for example the subgroup $G$ of $\operatorname{\rm SL}(3,\mathbb{Z})$ consisting of upper triangular matrices with ones on the diagonal, with $G_1$ the central copy of $\mathbb{Z}$ in the top right corner. Any extra properties you require had better not be satisfied by this mild looking group.
Jan 17 at 12:04	history	edited	Marcos	CC BY-SA 4.0	deleted 2 characters in body
Jan 17 at 11:51	history	edited	Marcos	CC BY-SA 4.0	deleted 91 characters in body
Jan 17 at 11:45	history	asked	Marcos	CC BY-SA 4.0