Question

Question on isomorphisms : is this true $\mathbb{Q}/\mathbb{Z}\le\mathbb{T}$?

score 23 · Answer 1 · 2016-10-08 03:41:48

23

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Question on isomorphisms : is this true $\mathbb{Q}/\mathbb{Z}\le\mathbb{T}$?

Published on 08 Oct 2016 - 3:41

score 556 · Answer 2 · 2026-03-30 17:53:22

556

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Is there any elegent way to formally prove that the ring $\mathbb Z/(8)$ cannot be decomposed to a product of rings?

Published on 30 Mar 2026 - 17:53

score 151 · Answer 3 · 2026-03-30 23:19:11

151

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Normal Subgroups, quotient groups

Published on 30 Mar 2026 - 23:19

score 2.4k · Answer 4 · 2026-03-29 07:29:17

2.4k

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If $\phi: G\rightarrow G'$ be a group onto homomorphism then show that $|G'|$ divides $|G|$

Published on 29 Mar 2026 - 7:29

score 3.2k · Answer 5 · 2026-03-29 07:33:48

3.2k

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Find some permutation group(s) isomorphic to Klein's 4-group**

Published on 29 Mar 2026 - 7:33

score 116 · Answer 6 · 2016-10-11 09:19:49

116

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Prove that α is an automorphism of $\mathbb{Z}_n \to \mathbb{Z}_n$.

Published on 11 Oct 2016 - 9:19

score 1.1k · Answer 7 · 2016-10-12 01:57:45

1.1k

Views

What are the two groups that are bijective, but not isomorphic?

Published on 12 Oct 2016 - 1:57

score 57 · Answer 8 · 2016-10-13 01:00:34

57

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$H_p(K)$ and $H_p(K^r)$ are isomorphic

Published on 13 Oct 2016 - 1:00

score 162 · Answer 9 · 2016-10-13 02:23:37

162

Views

Extension of isomorphism

Published on 13 Oct 2016 - 2:23

score 62 · Answer 10 · 2026-03-29 07:33:47

62

Views

Show Composition Map $S_3 \to S_4/V$ is an isomorphism.

Published on 29 Mar 2026 - 7:33

score 39 · Answer 11 · 2016-10-15 04:06:34

39

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Does $\mathbb{Z}_{p^3}$ have a subgroup isomorphic to $\mathbb{Z}_p \oplus \mathbb{Z}_p$?

Published on 15 Oct 2016 - 4:06

score 588 · Answer 12 · 2026-03-28 18:12:54

588

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Finding Explicit isomorphism

Published on 28 Mar 2026 - 18:12

score 1.1k · Answer 13 · 2026-03-29 09:47:13

1.1k

Views

Proving an isomorphism without a defined function

Published on 29 Mar 2026 - 9:47

score 136 · Answer 14 · 2026-03-31 04:05:33

136

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For $x,y \in \mathbb{Q}\setminus\{ 0\}$, prove that $\mathbb{Q}/\langle x \rangle \simeq \mathbb{Q}/ \langle y \rangle$.

Published on 31 Mar 2026 - 4:05

score 91 · Answer 15 · 2016-10-19 22:01:24

91

Views

For the following group how to prove no two of them are isomorphic?

Published on 19 Oct 2016 - 22:01

List Question

Question on isomorphisms : is this true $\mathbb{Q}/\mathbb{Z}\le\mathbb{T}$?

Is there any elegent way to formally prove that the ring $\mathbb Z/(8)$ cannot be decomposed to a product of rings?

Normal Subgroups, quotient groups

If $\phi: G\rightarrow G'$ be a group onto homomorphism then show that $|G'|$ divides $|G|$

Find some permutation group(s) isomorphic to Klein's 4-group**

Prove that α is an automorphism of $\mathbb{Z}_n \to \mathbb{Z}_n$.

What are the two groups that are bijective, but not isomorphic?

$H_p(K)$ and $H_p(K^r)$ are isomorphic

Extension of isomorphism

Show Composition Map $S_3 \to S_4/V$ is an isomorphism.

Does $\mathbb{Z}_{p^3}$ have a subgroup isomorphic to $\mathbb{Z}_p \oplus \mathbb{Z}_p$?

Finding Explicit isomorphism

Proving an isomorphism without a defined function

For $x,y \in \mathbb{Q}\setminus\{ 0\}$, prove that $\mathbb{Q}/\langle x \rangle \simeq \mathbb{Q}/ \langle y \rangle$.

For the following group how to prove no two of them are isomorphic?

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