List questions from group-homomorphism

Published on 29 Mar 2026 - 5:35

148

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Group homomorphism between multiplicative groups of rings

Published on 23 Feb 2026 - 10:07

160

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If $g: G \rightarrow S_4$ is a group homomorphism with $|\ker g|=24$, then the group $G$ is solvable.

Published on 28 Mar 2026 - 8:09

144

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Show that the kernel of a homomorphism from $G_1*G_2$ to $G_1\times G_2$ is free on $S$

Published on 30 Mar 2026 - 4:58

107

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Does there exists group isomorphism $ϕ: \Bbb Z_{40} \rightarrow \Bbb Z_{40}$ such that $ϕ(17) = 15$?

Published on 15 Jan 2022 - 11:48

313

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Let $G$ be a abelian group and $H\subseteq G$ is a subgroup. Prove: There exists homomorphism $Q$ such that $\ker Q=H$.

Published on 16 Jan 2022 - 16:16

53

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What Should the Formula for this Map Be?

Published on 18 Jan 2022 - 9:09

48

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Find all homomorphisms between $\mathbb{Z}_n$ and $\mathbb{C} \setminus \{0\}$

Published on 19 Jan 2022 - 0:37

328

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Quotient group of $\mathbb{C^*}$ by $n$th roots of unity

Published on 29 Mar 2026 - 7:29

146

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Number of homomorphisms from $\mathbb Z_5 \times \mathbb Z_5 \times \mathbb Z_5$ to $S_5$ and backwards

Published on 23 Jan 2022 - 7:38

94

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Algebraic group scheme is a torsor under kernel of a group homomorphism.

Published on 24 Jan 2022 - 20:54

117

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Given homomorphism $f(x)=x^m$, when is $f$ isomorphism over finite Abelian group?

Published on 27 Jan 2022 - 14:31

68

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If $\pi: G \to H/K$ such that $\pi (g) = \varphi(g)K$, prove that it is well-defined.

Published on 30 Mar 2026 - 13:57

51

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Changing base to "diagonalize" a rectangular matrix

Published on 02 Feb 2022 - 13:55

77

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Prove $\theta:S\to E^G$ is $R$-module isomorphism

Published on 25 Mar 2026 - 22:10

List Question

Centers and Quotients of Groups

Group homomorphism between multiplicative groups of rings

If $g: G \rightarrow S_4$ is a group homomorphism with $|\ker g|=24$, then the group $G$ is solvable.

Show that the kernel of a homomorphism from $G_1*G_2$ to $G_1\times G_2$ is free on $S$

Does there exists group isomorphism $ϕ: \Bbb Z_{40} \rightarrow \Bbb Z_{40}$ such that $ϕ(17) = 15$?

Let $G$ be a abelian group and $H\subseteq G$ is a subgroup. Prove: There exists homomorphism $Q$ such that $\ker Q=H$.

What Should the Formula for this Map Be?

Find all homomorphisms between $\mathbb{Z}_n$ and $\mathbb{C} \setminus \{0\}$

Quotient group of $\mathbb{C^*}$ by $n$th roots of unity

Number of homomorphisms from $\mathbb Z_5 \times \mathbb Z_5 \times \mathbb Z_5$ to $S_5$ and backwards

Algebraic group scheme is a torsor under kernel of a group homomorphism.

Given homomorphism $f(x)=x^m$, when is $f$ isomorphism over finite Abelian group?

If $\pi: G \to H/K$ such that $\pi (g) = \varphi(g)K$, prove that it is well-defined.

Changing base to "diagonalize" a rectangular matrix

Prove $\theta:S\to E^G$ is $R$-module isomorphism

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