List questions from group-homomorphism

Published on 26 May 2020 - 2:17

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prove that function mapping is injective iff ker (f) = {e}

Published on 26 Mar 2026 - 19:15

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Counterexample: Two groups $H$ and $G$, with surjective homomorphismus

Published on 28 May 2020 - 19:44

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Induced homomorphism example

Published on 01 Jun 2020 - 19:37

42

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Question regarding surjectivity of induced homormophism in an old version of Hatcher's proof of Prop. 4.13

Published on 25 Mar 2026 - 4:43

230

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Proving $xRy\iff xy^{-1}\in\ker(f)$ is equivalent relation, where $f:(G,.) \to (H,.)$ is homomorphism of groups $G$ and $H$.

Published on 03 Jun 2020 - 11:18

105

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Finding isomorphism between two groups

Published on 26 Mar 2026 - 16:02

183

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isomorphism between a field and non-field rings

Published on 05 Jun 2020 - 5:19

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Why is it the (group) morphisms that matter?

Published on 08 Jun 2020 - 20:54

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Find all group homomorphisms $A_n \rightarrow \mathbb{C}^*$

Published on 09 Jun 2020 - 11:12

239

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Find all the endomorphisms of the multiplicative group $\mathbb R^+$.

Published on 11 Jun 2020 - 13:53

477

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Homomorphism From a Finite to an Infinite Group

Published on 11 Jun 2020 - 21:34

268

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Prove that if there is a nontrivial homomorphism from $D_n$ to G then the order of G is even.

Published on 26 Mar 2026 - 17:47

162

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For any $n \in \Bbb N$, for any representation $\phi:SL_2(\Bbb R) \to U(n)$ we must have $\phi \begin{pmatrix} 0 &1 \\ -1 &0 \end{pmatrix}= I_{n}$

Published on 25 Mar 2026 - 22:05

158

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Find a homomorphism $f : H \to S_n$ such that $N = \ker(f)$.

Published on 18 Jun 2020 - 14:46

List Question

Proving that the restriction of a homomorphic function is also a homomorphism

prove that function mapping is injective iff ker (f) = {e}

Counterexample: Two groups $H$ and $G$, with surjective homomorphismus

Induced homomorphism example

Question regarding surjectivity of induced homormophism in an old version of Hatcher's proof of Prop. 4.13

Proving $xRy\iff xy^{-1}\in\ker(f)$ is equivalent relation, where $f:(G,.) \to (H,.)$ is homomorphism of groups $G$ and $H$.

Finding isomorphism between two groups

isomorphism between a field and non-field rings

Why is it the (group) morphisms that matter?

Find all group homomorphisms $A_n \rightarrow \mathbb{C}^*$

Find all the endomorphisms of the multiplicative group $\mathbb R^+$.

Homomorphism From a Finite to an Infinite Group

Prove that if there is a nontrivial homomorphism from $D_n$ to G then the order of G is even.

For any $n \in \Bbb N$, for any representation $\phi:SL_2(\Bbb R) \to U(n)$ we must have $\phi \begin{pmatrix} 0 &1 \\ -1 &0 \end{pmatrix}= I_{n}$

Find a homomorphism $f : H \to S_n$ such that $N = \ker(f)$.

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