List questions from group-homomorphism

Published on 20 Mar 2026 - 11:40

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Order of a group = Order of kernel × Order of homomorphic image?

Published on 20 Mar 2026 - 16:39

876

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Construct a non trivial homomorphism $\mathbb Z_{14} \to\mathbb Z_{21}$

Published on 22 Mar 2026 - 8:10

219

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Continuous group homomorphism between normed vector spaces are linear?

Published on 20 Mar 2026 - 18:09

299

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Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

Published on 19 Mar 2026 - 4:31

259

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Coset and Fiber

Published on 19 Mar 2026 - 23:01

73

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Finding a homormorphism form $\mathbb{Z}/4\mathbb{Z}$ to $\mathbb{Z}/6\mathbb{Z}$

Published on 20 Mar 2026 - 8:48

51

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Show that the element $φ(a)\in G'$ has also order d!

Published on 20 Mar 2026 - 21:05

85

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Explicit description of the group of homomorphisms from $\mathbb{Z}_p^{\times}$ to $\mathbb{Z}/n$

Published on 20 Mar 2026 - 9:44

54

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Smallest $n\in \mathbb{Z}_{>0}$ for existence of a monomorphism $G \rightarrow S_n$

Published on 19 Mar 2026 - 21:57

131

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What breaks if I use a $G$-module instead of a $\mathbb{K}[G]$-module: Induced reps, Frobenius reciprocity?

Published on 22 Mar 2026 - 8:29

189

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Finding a representation of $D_n$ on $\mathbb{R}^2$?

Published on 24 Mar 2026 - 22:01

68

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Decomposition of the representation $\chi_m(t)=e^{imt}$?

Published on 24 Mar 2026 - 22:09

170

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Counting homomorphism between groups

Published on 25 Mar 2026 - 2:57

75

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Show that, for every $x\ \epsilon \ C_{m}$, we have that $ord(f(x))$ is a divisor of d.

Published on 20 Mar 2026 - 22:34

List Question

homomorphism between unitary groups

Order of a group = Order of kernel × Order of homomorphic image?

Construct a non trivial homomorphism $\mathbb Z_{14} \to\mathbb Z_{21}$

Continuous group homomorphism between normed vector spaces are linear?

Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

Coset and Fiber

Finding a homormorphism form $\mathbb{Z}/4\mathbb{Z}$ to $\mathbb{Z}/6\mathbb{Z}$

Show that the element $φ(a)\in G'$ has also order d!

Explicit description of the group of homomorphisms from $\mathbb{Z}_p^{\times}$ to $\mathbb{Z}/n$

Smallest $n\in \mathbb{Z}_{>0}$ for existence of a monomorphism $G \rightarrow S_n$

What breaks if I use a $G$-module instead of a $\mathbb{K}[G]$-module: Induced reps, Frobenius reciprocity?

Finding a representation of $D_n$ on $\mathbb{R}^2$?

Decomposition of the representation $\chi_m(t)=e^{imt}$?

Counting homomorphism between groups

Show that, for every $x\ \epsilon \ C_{m}$, we have that $ord(f(x))$ is a divisor of d.

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