List questions from hopfian

Published on 23 Feb 2026 - 15:10

265

Views

Must a surjection $F_2\to F_2$ also be an injection?

Published on 23 Feb 2026 - 15:09

1.2k

Views

Homomorphism/map in both direction implies isomorphism/homeomorphism or not?

Published on 23 Feb 2026 - 15:06

1.3k

Views

If $G$ is a group and $N$ is a nontrivial normal subgroup, can $G/N \cong G$?

Published on 23 Feb 2026 - 15:09

939

Views

An example of a residually finite group which is not Hopf

Published on 23 Feb 2026 - 15:09

683

Views

Is a free group of finite rank Hopfian?

Published on 23 Feb 2026 - 15:09

210

Views

Is retract of a finitely generated Hopfian group Hopfian?

Published on 09 Apr 2026 - 16:20

154

Views

Is a finitely generated module over a Hopfian ring Hopfian?

Published on 23 Feb 2026 - 15:07

1.3k

Views

The free group $F_3$ being a quotient of $F_2$

Published on 23 Feb 2026 - 15:09

547

Views

Epimorphism from GL(2,Z) to GL(2,Z)

Published on 23 Feb 2026 - 15:07

291

Views

$\langle X|\emptyset\rangle\ncong\langle X|R\rangle$ for finitely presented groups (exercise in Massey)

Published on 23 Feb 2026 - 15:08

1.4k

Views

When can a pair of groups be embedded in each other?

Published on 23 Feb 2026 - 15:06

621

Views

The Hopfian property for groups

Published on 05 Apr 2026 - 22:38

6.4k

Views

Does $G\cong G/H$ imply that $H$ is trivial?

Published on 08 Apr 2026 - 23:49

2.5k

Views

Can you always find a surjective endomorphism of groups such that it is not injective?

Published on 23 Feb 2026 - 15:09

List Question

To prove that a hopfian group is not free.

Must a surjection $F_2\to F_2$ also be an injection?

Homomorphism/map in both direction implies isomorphism/homeomorphism or not?

If $G$ is a group and $N$ is a nontrivial normal subgroup, can $G/N \cong G$?

An example of a residually finite group which is not Hopf

Is a free group of finite rank Hopfian?

Is retract of a finitely generated Hopfian group Hopfian?

Is a finitely generated module over a Hopfian ring Hopfian?

The free group $F_3$ being a quotient of $F_2$

Epimorphism from GL(2,Z) to GL(2,Z)

$\langle X|\emptyset\rangle\ncong\langle X|R\rangle$ for finitely presented groups (exercise in Massey)

When can a pair of groups be embedded in each other?

The Hopfian property for groups

Does $G\cong G/H$ imply that $H$ is trivial?

Can you always find a surjective endomorphism of groups such that it is not injective?

Trending Questions

Popular # Hahtags

Popular Questions