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Proof question: Show there is no homomorphism from $\Bbb Z_{16} \oplus \Bbb Z_{2}$ onto $\Bbb Z_4 \oplus \Bbb Z_4$

score 815 · Answer 1 · 2016-08-24 19:42:27

815

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Proof question: Show there is no homomorphism from $\Bbb Z_{16} \oplus \Bbb Z_{2}$ onto $\Bbb Z_4 \oplus \Bbb Z_4$

Published on 24 Aug 2016 - 19:42

score 104 · Answer 2 · 2026-03-26 06:32:41

104

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$H,K$ be subgroups of an infinite abelian group $G$ such that $K \subseteq H$ and $G \cong K$ , then is it true that $G\cong H$ ?

Published on 26 Mar 2026 - 6:32

score 147 · Answer 3 · 2016-08-29 06:51:55

147

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$\operatorname{Hom}(G_1 \times ... \times G_k,G) \cong \operatorname{Hom}(G_1,G) \times....\times \mathrm{Hom}(G_k,G)$ where $G_i,G$ are groups?

Published on 29 Aug 2016 - 6:51

score 281 · Answer 4 · 2016-08-29 07:05:32

281

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Why is $\phi(x^i)=y^i$ not a group homomorphism between the cyclic group of order $36$ to the cyclic group of order $17$?

Published on 29 Aug 2016 - 7:05

score 32 · Answer 5 · 2016-09-08 19:48:17

32

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Finding all homomorphisms from $\mu_{12}$ to $\mu_6$

Published on 08 Sep 2016 - 19:48

score 781 · Answer 6 · 2016-09-12 11:17:51

781

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The symmetric group of $\mathbb{Z}$ is isomorphic to which group?

Published on 12 Sep 2016 - 11:17

score 67 · Answer 7 · 2026-03-26 19:23:43

67

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Extending a homomorphism

Published on 26 Mar 2026 - 19:23

score 64 · Answer 8 · 2026-03-26 08:02:22

64

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Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

Published on 26 Mar 2026 - 8:02

score 693 · Answer 9 · 2016-09-17 09:16:45

693

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number of homomorphisms from a group to another

Published on 17 Sep 2016 - 9:16

score 1.1k · Answer 10 · 2016-09-17 19:40:16

1.1k

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Mapping Generators to Generators

Published on 17 Sep 2016 - 19:40

score 111 · Answer 11 · 2016-09-17 21:26:44

111

Views

How could I prove that Aut$(C_n) = (\mathbb{Z}/n)^*$

Published on 17 Sep 2016 - 21:26

score 446 · Answer 12 · 2016-09-18 10:09:13

446

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Is any subgroup normal?

Published on 18 Sep 2016 - 10:09

score 740 · Answer 13 · 2016-09-18 23:30:55

740

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How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

Published on 18 Sep 2016 - 23:30

score 201 · Answer 14 · 2016-09-19 03:49:46

201

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Kernel is a normal subgroup of the preimage

Published on 19 Sep 2016 - 3:49

score 1.7k · Answer 15 · 2016-09-19 05:53:38

1.7k

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Concrete example of an endomorphism ring?

Published on 19 Sep 2016 - 5:53

List Question

Proof question: Show there is no homomorphism from $\Bbb Z_{16} \oplus \Bbb Z_{2}$ onto $\Bbb Z_4 \oplus \Bbb Z_4$

$H,K$ be subgroups of an infinite abelian group $G$ such that $K \subseteq H$ and $G \cong K$ , then is it true that $G\cong H$ ?

$\operatorname{Hom}(G_1 \times ... \times G_k,G) \cong \operatorname{Hom}(G_1,G) \times....\times \mathrm{Hom}(G_k,G)$ where $G_i,G$ are groups?

Why is $\phi(x^i)=y^i$ not a group homomorphism between the cyclic group of order $36$ to the cyclic group of order $17$?

Finding all homomorphisms from $\mu_{12}$ to $\mu_6$

The symmetric group of $\mathbb{Z}$ is isomorphic to which group?

Extending a homomorphism

Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

number of homomorphisms from a group to another

Mapping Generators to Generators

How could I prove that Aut$(C_n) = (\mathbb{Z}/n)^*$

Is any subgroup normal?

How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

Kernel is a normal subgroup of the preimage

Concrete example of an endomorphism ring?

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