List questions from group-homomorphism

Published on 25 Nov 2020 - 22:46

182

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Group homomorphism between $\mathbb Z/n\mathbb Z$ and $S_n$.

Published on 26 Nov 2020 - 15:48

51

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Induced Homomorphism in the unit circle

Published on 26 Nov 2020 - 15:53

179

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Is $\phi:\mathbb{Z}_5\to\mathbb{Z}_{30},$ $\phi(x)=6x$ a homomorphism?

Published on 27 Nov 2020 - 1:36

71

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Find kernel of a homomorphism $f$

Published on 27 Nov 2020 - 12:41

59

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Find a non-abelian group such that $(ab)^{12} = a^{12} b^{12}$

Published on 27 Nov 2020 - 23:22

57

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Let $G,K$ be groups with $H\le G$. It is not always possible to extend a homomorphism $\sigma:H\to K$ to $G$

Published on 27 Nov 2020 - 23:47

664

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Prove that $G= \ker(f) \times{\rm im}(f)$

Published on 30 Nov 2020 - 2:12

127

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Endomorphism that maps Center to "not Center"

Published on 30 Nov 2020 - 4:51

120

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If $\theta :G\rightarrow H$ is a surjective homomorphism, then $\theta(\Phi(G))\leq\Phi(H)$.

Published on 25 Mar 2026 - 7:45

69

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Homomorphism from $D_n$ to $D_{\infty}$

Published on 29 Mar 2026 - 0:06

71

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Homomorphisms from $\textrm{Af}_1(\mathbb{R})$ to $(\mathbb{R}, +)$

Published on 30 Mar 2026 - 9:47

135

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If a homomorphism is surjective it cannot be trivial

Published on 02 Dec 2020 - 20:09

196

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Consequence of induced homomorphism of covering map being trivial?

Published on 03 Dec 2020 - 0:38

313

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Let ${\rm Hom}:G\to G'$ be a homomorphism. Prove that if $H\unlhd G$ then ${\rm Hom}(H)\unlhd G'$.

Published on 05 Dec 2020 - 21:30

List Question

Homomorphism between $Q_8$ and $S_4$

Group homomorphism between $\mathbb Z/n\mathbb Z$ and $S_n$.

Induced Homomorphism in the unit circle

Is $\phi:\mathbb{Z}_5\to\mathbb{Z}_{30},$ $\phi(x)=6x$ a homomorphism?

Find kernel of a homomorphism $f$

Find a non-abelian group such that $(ab)^{12} = a^{12} b^{12}$

Let $G,K$ be groups with $H\le G$. It is not always possible to extend a homomorphism $\sigma:H\to K$ to $G$

Prove that $G= \ker(f) \times{\rm im}(f)$

Endomorphism that maps Center to "not Center"

If $\theta :G\rightarrow H$ is a surjective homomorphism, then $\theta(\Phi(G))\leq\Phi(H)$.

Homomorphism from $D_n$ to $D_{\infty}$

Homomorphisms from $\textrm{Af}_1(\mathbb{R})$ to $(\mathbb{R}, +)$

If a homomorphism is surjective it cannot be trivial

Consequence of induced homomorphism of covering map being trivial?

Let ${\rm Hom}:G\to G'$ be a homomorphism. Prove that if $H\unlhd G$ then ${\rm Hom}(H)\unlhd G'$.

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