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Results tagged with fibered-products
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user 197354
13
votes
2
answers
304
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Does a fibre product of a group $G$ with itself have a subgroup isomorphic to $G$?
Let $G$ be a group, and consider a fibre product of the form $H=G\times_{D,\phi,\psi}G$, i.e. the group of pairs $(g,g'),\phi(g)=\psi(g')$, for some surjective group morphisms $\phi:G\rightarrow D$ an …
- 173
4
votes
Does a fibre product of a group $G$ with itself have a subgroup isomorphic to $G$?
By mistake, I did not find any counterexample for the case of $G=D_4$. I have done the computations again, and this actually gives the smallest possible counterexample.
Let $r$ and $s$ be the usual ge …
- 173