List questions from group-homomorphism

Published on 21 Mar 2022 - 11:49

141

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Help understanding the use of the First Isomorphism Theorem with regards to the special linear group

Published on 29 Mar 2026 - 14:02

292

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Prove that ${\rm Inn}(S_n)$ isomorphic to $S_n.$

Published on 24 Mar 2022 - 1:35

64

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Draw a covering of $S^1 \vee S^1$ whose fundamental group is isomorphic to $\ker \Phi : F_2 \to \mathbb Z$ with $a\mapsto 2, b\mapsto 3$

Published on 30 Mar 2026 - 6:48

205

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Existence of a canonical isomorphism for ($\operatorname{Hom}$-$\otimes$ adjunction).

Published on 31 Mar 2022 - 15:17

54

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What’s going on when I restrict a homomorphism to a smaller quotient group?

Published on 29 Mar 2026 - 12:32

416

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How to construct an injective homomorphism from $GL(2,\mathbb{Z}_2)$ into $S_4$?

Published on 04 Apr 2022 - 15:17

101

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Understanding homomorphism and non-homomorphism from $A_4$ to $S_6$

Published on 07 Apr 2022 - 9:43

174

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Quotient group by normal closure of union

Published on 29 Mar 2026 - 10:48

71

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Is $\ker\varphi^2=(\ker\varphi)(\mathop{\rm im}\varphi\cap\ker\varphi^2)$ always true for group endomorphism $\varphi$?

Published on 01 Apr 2026 - 21:30

49

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Why does injectivity imply to $|G/(H \cap K)|\leq |G/H|\cdot|G/K|?$

Published on 29 Mar 2026 - 14:07

51

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For any finite group $H$ and homomorphism $\alpha:BS(2,3)\to H$, prove $\alpha([bab^{-1},a])=1$

Published on 30 Mar 2026 - 1:48

179

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Every action gives rise to a homomorphism

Published on 16 Apr 2022 - 12:46

71

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Proving isomorphism between two vector spaces of homomorphisms

Published on 17 Apr 2022 - 12:21

145

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Yes/No: There always exists an injective homomorphism from $G$ into $S_n$.

Published on 18 Apr 2022 - 10:33

List Question

A conditioned morphism in a group

Help understanding the use of the First Isomorphism Theorem with regards to the special linear group

Prove that ${\rm Inn}(S_n)$ isomorphic to $S_n.$

Draw a covering of $S^1 \vee S^1$ whose fundamental group is isomorphic to $\ker \Phi : F_2 \to \mathbb Z$ with $a\mapsto 2, b\mapsto 3$

Existence of a canonical isomorphism for ($\operatorname{Hom}$-$\otimes$ adjunction).

What’s going on when I restrict a homomorphism to a smaller quotient group?

How to construct an injective homomorphism from $GL(2,\mathbb{Z}_2)$ into $S_4$?

Understanding homomorphism and non-homomorphism from $A_4$ to $S_6$

Quotient group by normal closure of union

Is $\ker\varphi^2=(\ker\varphi)(\mathop{\rm im}\varphi\cap\ker\varphi^2)$ always true for group endomorphism $\varphi$?

Why does injectivity imply to $|G/(H \cap K)|\leq |G/H|\cdot|G/K|?$

For any finite group $H$ and homomorphism $\alpha:BS(2,3)\to H$, prove $\alpha([bab^{-1},a])=1$

Every action gives rise to a homomorphism

Proving isomorphism between two vector spaces of homomorphisms

Yes/No: There always exists an injective homomorphism from $G$ into $S_n$.

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