List questions from group-homomorphism

Published on 25 Mar 2026 - 22:11

46

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Suppose $\#N = 5$. If $f: G \to \mathbb{Z} / 6 \mathbb{Z}$ is a surjective homomorphism, what are the possible orders for the group $G$?

Published on 02 Jun 2021 - 12:43

1.1k

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Extending homomorphism on subgroup to the whole group

Published on 07 Jun 2021 - 18:39

83

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Show that $\phi(K)=KN/N$

Published on 28 Mar 2026 - 21:06

309

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Homomorphism and Holomorphic Functions

Published on 31 Mar 2026 - 12:12

64

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Fundamental theorem on homomorphisms for structures with only identity element

Published on 19 Jun 2021 - 12:53

98

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If $A\unlhd B$, then prove that $A\phi\unlhd B\phi$ for a homomorphism $\phi$.

Published on 26 Jun 2021 - 16:58

60

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The image of a completely reducible group is itself completely reducible.

Published on 28 Mar 2026 - 13:41

379

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How is injectivity enough to show function is an isomorphism?

Published on 29 Jun 2021 - 12:35

112

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Show ${\rm Hom}(A\times B,C\times D)\cong{\rm Hom}(A,C)\times{\rm Hom}(A,D)\times{\rm Hom}(B,C)\times{\rm Hom}(B,D),$

Published on 03 Jul 2021 - 10:27

156

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Let $G$ and $H$ be groups and let $f :G \to H$ be a group homomorphism. Show that $\ker(f)$ is a normal subgroup of $G$.

Published on 06 Jul 2021 - 11:17

49

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Is this module torsion?

Published on 27 Mar 2026 - 0:55

50

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Representation between two groups

Published on 13 Jul 2021 - 12:40

86

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find the number of homomorphisms from $\mathbb{Z_{3}}\times\mathbb{Z_{4}}\times\mathbb{Z_{9}}$ to $\mathbb{Z_{18}}$

Published on 18 Jul 2021 - 11:52

110

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Group homomorphism intuition

Published on 26 Jul 2021 - 11:17

List Question

Hom( , ) and Hom_F( , ) and tensor product

Suppose $\#N = 5$. If $f: G \to \mathbb{Z} / 6 \mathbb{Z}$ is a surjective homomorphism, what are the possible orders for the group $G$?

Extending homomorphism on subgroup to the whole group

Show that $\phi(K)=KN/N$

Homomorphism and Holomorphic Functions

Fundamental theorem on homomorphisms for structures with only identity element

If $A\unlhd B$, then prove that $A\phi\unlhd B\phi$ for a homomorphism $\phi$.

The image of a completely reducible group is itself completely reducible.

How is injectivity enough to show function is an isomorphism?

Show ${\rm Hom}(A\times B,C\times D)\cong{\rm Hom}(A,C)\times{\rm Hom}(A,D)\times{\rm Hom}(B,C)\times{\rm Hom}(B,D),$

Let $G$ and $H$ be groups and let $f :G \to H$ be a group homomorphism. Show that $\ker(f)$ is a normal subgroup of $G$.

Is this module torsion?

Representation between two groups

find the number of homomorphisms from $\mathbb{Z_{3}}\times\mathbb{Z_{4}}\times\mathbb{Z_{9}}$ to $\mathbb{Z_{18}}$

Group homomorphism intuition

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