List questions from group-homomorphism

Published on 22 Oct 2019 - 0:37

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Every homomorphic image of abelian group is abelian but converse need not be true.

Published on 22 Oct 2019 - 17:04

489

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Endomorphisms of $\mathbb Z_4$

Published on 23 Oct 2019 - 7:14

472

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Intuition with the Inverse Quotient Map

Published on 26 Mar 2026 - 2:54

79

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Why is the induced homomorphism on the abelianisation of groups well defined?

Published on 25 Oct 2019 - 21:25

127

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Let $G$ be infinite group, $f$ be automorphism with only one fixed point identity.

Published on 27 Oct 2019 - 8:38

54

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Homological Algebra: R-homomorphism

Published on 27 Oct 2019 - 14:22

69

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Homological Algebra: monomorphism

Published on 27 Oct 2019 - 16:19

46

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How the existence of a special homomorphism of a group can help me constract a special normal subgroup to represent uniquely the group?

Published on 28 Oct 2019 - 10:42

280

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Every homomorphism $A_n\to S_n$ extends to an endomorphism of $S_n$ for $n\geq 5$

Published on 30 Oct 2019 - 14:09

184

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Find all homomorphisms $S_3 \rightarrow \mathbb Z_2 \oplus \mathbb Z_2 \oplus \mathbb Z_3$

Published on 30 Oct 2019 - 23:42

149

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Working with Isometries in $\mathbb{R}^2$

Published on 25 Mar 2026 - 23:56

694

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Does there exist a surjective group homomorphism from G to H such that G doesn't contain a subgroup isomorphic to H?

Published on 31 Oct 2019 - 19:07

111

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Is the trivial homomorphic image of a field a ring?

Published on 25 Mar 2026 - 14:34

41

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Group homomorphism between $\mathbb{Z}/n\Bbb Z$ and $\mathbb{Z}$ must be zero

Published on 26 Mar 2026 - 2:55

List Question

Proof of fundamental theorem for group homomorphisms

Every homomorphic image of abelian group is abelian but converse need not be true.

Endomorphisms of $\mathbb Z_4$

Intuition with the Inverse Quotient Map

Why is the induced homomorphism on the abelianisation of groups well defined?

Let $G$ be infinite group, $f$ be automorphism with only one fixed point identity.

Homological Algebra: R-homomorphism

Homological Algebra: monomorphism

How the existence of a special homomorphism of a group can help me constract a special normal subgroup to represent uniquely the group?

Every homomorphism $A_n\to S_n$ extends to an endomorphism of $S_n$ for $n\geq 5$

Find all homomorphisms $S_3 \rightarrow \mathbb Z_2 \oplus \mathbb Z_2 \oplus \mathbb Z_3$

Working with Isometries in $\mathbb{R}^2$

Does there exist a surjective group homomorphism from G to H such that G doesn't contain a subgroup isomorphic to H?

Is the trivial homomorphic image of a field a ring?

Group homomorphism between $\mathbb{Z}/n\Bbb Z$ and $\mathbb{Z}$ must be zero

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