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Apr 27, 2017 at 7:59 comment added Xiaoyang Chen I see, in your mentioned example, take $g=(id, f), f \in Aut (H)$ such that $f_*: \pi_1(H) \rightarrow \pi_1(H)$ is not identity (or not a nilpotent group action), then $(Ad_g)_*: \pi_1(G) \rightarrow \pi_1(G) $ is also not identity (or not a nilpotent group action), right?
Apr 27, 2017 at 6:24 comment added Wilberd van der Kallen Consider the semi-direct product $G$ of a product $H$ of circle groups with any finite subgroup of the automorphism group of $H$.
Apr 27, 2017 at 4:45 history asked Xiaoyang Chen CC BY-SA 3.0