List questions from group-homomorphism

Published on 26 Sep 2020 - 4:23

840

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Generators of $S_4$

Published on 26 Sep 2020 - 11:27

316

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Prove that a function is not a homomorphism

Published on 27 Sep 2020 - 0:34

575

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group extension properties: split, central, cocycle or not

Published on 26 Mar 2026 - 7:57

93

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For a group homomorphism $f: G \to G'$, show that if $H < G$, then $f(H) \leq G'$.

Published on 28 Sep 2020 - 10:29

90

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If $H \leq G$ and $\ker (f) \subseteq H$, then $f^{-1} (f(H)) = H$

Published on 28 Sep 2020 - 14:43

27

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Show that $G / H \simeq G^{\prime} .$ Hence show that there does not exist any homomorphism from $Z_{9}$ onto $Z_{6}$

Published on 01 Oct 2020 - 7:01

53

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If $F$ is a field then prove that both $(F,+)$ and $(F^*,.)$ can be embedded in $SL_2(F)$

Published on 05 Oct 2020 - 12:31

125

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Checking that the given function is really a homomorphism.

Published on 25 Mar 2026 - 16:06

65

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Proving that the stabilizer of $\{2,4,6\}$ in $D_{6}$ is isomorphic to $S_{3}.$

Published on 29 Mar 2026 - 3:35

64

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Problems involving endomorphism of groups

Published on 31 Mar 2026 - 8:07

45

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Question involving the homomorphism theorem and group theory.

Published on 09 Oct 2020 - 1:25

263

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Show that $\phi$ is a homomorphism using modular arithmetic

Published on 09 Oct 2020 - 4:02

74

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Express generator of kernel in terms of basis vectors

Published on 09 Oct 2020 - 6:05

181

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All homorphisms that are isomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

Published on 11 Oct 2020 - 4:50

List Question

Prove whether it is a homomorphism.

Generators of $S_4$

Prove that a function is not a homomorphism

group extension properties: split, central, cocycle or not

For a group homomorphism $f: G \to G'$, show that if $H < G$, then $f(H) \leq G'$.

If $H \leq G$ and $\ker (f) \subseteq H$, then $f^{-1} (f(H)) = H$

Show that $G / H \simeq G^{\prime} .$ Hence show that there does not exist any homomorphism from $Z_{9}$ onto $Z_{6}$

If $F$ is a field then prove that both $(F,+)$ and $(F^*,.)$ can be embedded in $SL_2(F)$

Checking that the given function is really a homomorphism.

Proving that the stabilizer of $\{2,4,6\}$ in $D_{6}$ is isomorphic to $S_{3}.$

Problems involving endomorphism of groups

Question involving the homomorphism theorem and group theory.

Show that $\phi$ is a homomorphism using modular arithmetic

Express generator of kernel in terms of basis vectors

All homorphisms that are isomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

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