List questions from group-homomorphism

Published on 24 May 2019 - 2:07

30

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Proof: There is exactly one matrix $B\in K^{n\times m}, AB=I_m$ if $\varphi$ is surjective

Published on 26 May 2019 - 18:56

1.7k

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Find all homomorphisms $φ : \mathbb{Z} → \mathbb{Z}$. Which of these homomorphisms are isomorphisms?

Published on 27 May 2019 - 16:50

137

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using the kernel/cokernel to minimally adjust a homomorphism of abelian groups

Published on 29 May 2019 - 2:16

80

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How to prove that a set is universe of a subgroup?

Published on 04 Jun 2019 - 21:52

77

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Reference Request: An operation preserving bijection from a magma to a group must be a group isomorphism

Published on 23 Feb 2026 - 1:05

92

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Product, homomorphism and kernel of these two additive matrices groups

Published on 08 Jun 2019 - 11:41

218

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The Kernel of a Homomorphism

Published on 09 Jun 2019 - 18:49

1.2k

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The homomorphism associated to congruence modulo n

Published on 09 Jun 2019 - 19:41

94

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composition of permutations example

Published on 09 Jun 2019 - 20:49

33

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Subgroup automorphisms

Published on 25 Mar 2026 - 20:40

29

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Show that $\dim H^1(\Gamma(11)) = 3$

Published on 26 Mar 2026 - 4:52

126

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Is there a group G of order 20 such that there exists a surjective homomorphism $\phi: G \rightarrow \mathbb{Z}_{15}$?

Published on 19 Jun 2019 - 16:10

3.9k

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When is a bijective homomorphism an isomorphism?

Published on 25 Mar 2026 - 13:52

90

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Finding a Group isomorphism G

Published on 22 Jun 2019 - 8:55

List Question

Determine whether there is an onto homomorphism from $(\mathbb{Z}_6,+)$ to $(\mathrm{Z}_3,+)$

Proof: There is exactly one matrix $B\in K^{n\times m}, AB=I_m$ if $\varphi$ is surjective

Find all homomorphisms $φ : \mathbb{Z} → \mathbb{Z}$. Which of these homomorphisms are isomorphisms?

using the kernel/cokernel to minimally adjust a homomorphism of abelian groups

How to prove that a set is universe of a subgroup?

Reference Request: An operation preserving bijection from a magma to a group must be a group isomorphism

Product, homomorphism and kernel of these two additive matrices groups

The Kernel of a Homomorphism

The homomorphism associated to congruence modulo n

composition of permutations example

Subgroup automorphisms

Show that $\dim H^1(\Gamma(11)) = 3$

Is there a group G of order 20 such that there exists a surjective homomorphism $\phi: G \rightarrow \mathbb{Z}_{15}$?

When is a bijective homomorphism an isomorphism?

Finding a Group isomorphism G

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