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edit approved Sep 27, 2013 at 8:45
Sergiy Kozerenko
edit approved Sep 27, 2013 at 8:45
Sergiy Kozerenko
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Fix a finitely-presented group G$G$ with distinguished non-identity element g$g$. For any finitely-presented group H$H$ with element h$h$, is it decidable whether there is a homomorphism h: G -> H$h: G \rightarrow H$ such that h(g) = h?$h(g) = h\ ?$

If we know G$G$ is cyclic, the question is undecidable by reduction from the Word ProblemWord Problem. But what if we don't know anything about G$G$? What if we know g$g$ has finite order in G$G$?

Fix a finitely-presented group G with distinguished non-identity element g. For any finitely-presented group H with element h, is it decidable whether there is a homomorphism h: G -> H such that h(g) = h?

If we know G is cyclic, the question is undecidable by reduction from the Word Problem. But what if we don't know anything about G? What if we know g has finite order in G?

Fix a finitely-presented group $G$ with distinguished non-identity element $g$. For any finitely-presented group $H$ with element $h$, is it decidable whether there is a homomorphism $h: G \rightarrow H$ such that $h(g) = h\ ?$

If we know $G$ is cyclic, the question is undecidable by reduction from the Word Problem. But what if we don't know anything about $G$? What if we know $g$ has finite order in $G$?

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user667
user667
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decidability of group homomorphism existence

Fix a finitely-presented group G with distinguished non-identity element g. For any finitely-presented group H with element h, is it decidable whether there is a homomorphism h: G -> H such that h(g) = h?

If we know G is cyclic, the question is undecidable by reduction from the Word Problem. But what if we don't know anything about G? What if we know g has finite order in G?