List questions from hopfian

Published on 31 May 2016 - 8:04

264

Views

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

Published on 10 Apr 2013 - 9:13

1.2k

Views

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

Published on 08 Jun 2013 - 2:20

1.3k

Views

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

Published on 17 Nov 2013 - 8:43

938

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An example of a residually finite group which is not Hopf

Published on 10 Feb 2014 - 21:16

682

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Is a free group of finite rank Hopfian?

Published on 27 Sep 2017 - 16:38

209

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Is retract of a finitely generated Hopfian group Hopfian?

Published on 23 Feb 2026 - 12:07

153

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Is a finitely generated module over a Hopfian ring Hopfian?

Published on 02 Oct 2017 - 14:16

1.3k

Views

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

Published on 13 Dec 2010 - 21:07

546

Views

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

Published on 11 Jan 2011 - 17:54

290

Views

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

Published on 18 Aug 2011 - 9:41

1.4k

Views

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

Published on 07 Sep 2011 - 21:05

619

Views

The Hopfian property for groups

Published on 31 Oct 2011 - 15:23

6.4k

Views

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

Published on 07 Nov 2011 - 13:42

2.5k

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

Published on 17 Feb 2012 - 3:10

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?

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