List questions from hopfian

Published on 09 Apr 2018 - 17:02

337

Views

Groups $G$ for which every finitely generated $\mathbb{Z}G$-module is Hopfian

Published on 17 Jun 2018 - 7:52

250

Views

Is this surjective homomorphism necessarily injective? (Free Product of Cyclic groups)

Published on 03 Jul 2018 - 16:04

33

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If $G$ is a group and $\mathrm{End}(G) \cong \mathbb{Z},$ why is $G$ Hopfian?

Published on 15 Oct 2018 - 23:36

169

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Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).

Published on 05 Aug 2019 - 17:50

819

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Sort-of-simple non-Hopfian groups

Published on 25 Apr 2014 - 9:24

630

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Finitely generated abelian group is Hopfian.

Published on 26 Apr 2014 - 5:35

488

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Noetherian implies Hopfian

Published on 20 May 2014 - 4:53

120

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Hopfian and co-Hopfian groups

Published on 06 Nov 2014 - 14:35

74

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How do you prove that $BS(m,n)$ is hopfian when m and n have the same prime factors?

Published on 07 Oct 2019 - 16:05

74

Views

Hyperbolic groups are Hopfian

Published on 11 Jul 2023 - 8:21

56

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Is the Baumslag Solitair group B(2,3) really non-Hopfian?

Published on 31 Jul 2023 - 0:33

102

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Does $\mathbb{Z}* \mathbb{Z} /N = \mathbb{Z} * \mathbb{Z} \implies N$ is trivial?

Published on 14 Feb 2015 - 16:07

590

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(Non-Hopfian) groups that only have quotients that are themselves or the trivial group.

Published on 14 Jun 2015 - 9:31

65

Views

Groups with a dense chain of (isomorphic) subgroups

Published on 11 Apr 2016 - 16:14

List Question

A non co-hopfian simple group?

Groups $G$ for which every finitely generated $\mathbb{Z}G$-module is Hopfian

Is this surjective homomorphism necessarily injective? (Free Product of Cyclic groups)

If $G$ is a group and $\mathrm{End}(G) \cong \mathbb{Z},$ why is $G$ Hopfian?

Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).

Sort-of-simple non-Hopfian groups

Finitely generated abelian group is Hopfian.

Noetherian implies Hopfian

Hopfian and co-Hopfian groups

How do you prove that $BS(m,n)$ is hopfian when m and n have the same prime factors?

Hyperbolic groups are Hopfian

Is the Baumslag Solitair group B(2,3) really non-Hopfian?

Does $\mathbb{Z}* \mathbb{Z} /N = \mathbb{Z} * \mathbb{Z} \implies N$ is trivial?

(Non-Hopfian) groups that only have quotients that are themselves or the trivial group.

Groups with a dense chain of (isomorphic) subgroups

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