Question

Let $G=\mathbb{Z}\big /4\mathbb{Z}$ and $H=2\mathbb{Z}\big /4\mathbb{Z}$. Is $H$ isomorphic to $G\big / H$?

score 67 · Answer 1 · 2026-03-29 20:21:26

67

Views

Let $G=\mathbb{Z}\big /4\mathbb{Z}$ and $H=2\mathbb{Z}\big /4\mathbb{Z}$. Is $H$ isomorphic to $G\big / H$?

Published on 29 Mar 2026 - 20:21

score 40 · Answer 2 · 2026-04-09 12:53:54

40

Views

Inclusion induces homology group isomorphism

Published on 09 Apr 2026 - 12:53

score 106 · Answer 3 · 2026-03-25 14:21:21

106

Views

Why $E/AutE$ is isomorphic to $\Bbb{P}^1$?

Published on 25 Mar 2026 - 14:21

score 606 · Answer 4 · 2022-11-29 02:47:52

606

Views

Why are there only 5 abelian groups of order 48?

Published on 29 Nov 2022 - 2:47

score 116 · Answer 5 · 2026-04-09 02:37:40

116

Views

Show $\phi : S_3 \rightarrow S_3$ given by $\phi(f^{i}g^{j}) = f^{2i}g^{j}$ is an automorphism

Published on 09 Apr 2026 - 2:37

score 134 · Answer 6 · 2026-03-30 08:32:59

134

Views

Show $A_5 \cong \langle x,y \mid x^5,y^2,(xy)^3\rangle$

Published on 30 Mar 2026 - 8:32

score 292 · Answer 7 · 2022-12-05 09:54:13

292

Views

Understanding butterfly lemma and Isomorphism theorems

Published on 05 Dec 2022 - 9:54

score 58 · Answer 8 · 2022-12-07 09:02:29

58

Views

Prove that $[K : aHa^{-1} \cap K]$ is equal to number of left cosets of $H$ in $KaH$, where $K, H$ are subgroups of $G$ and $a\in G$

Published on 07 Dec 2022 - 9:02

score 133 · Answer 9 · 2026-04-02 07:56:55

133

Views

Is the number of homomorphisms between two isomorphic groups equals to the number of Automorphisms for each group?

Published on 02 Apr 2026 - 7:56

score 54 · Answer 10 · 2026-04-09 13:27:56

54

Views

Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Published on 09 Apr 2026 - 13:27

score 56 · Answer 11 · 2026-03-25 17:19:16

56

Views

Find all homomorphisms from $(\mathbb{Z}_8,+)$ into $(\mathbb{Z}_6,+)$.

Published on 25 Mar 2026 - 17:19

score 86 · Answer 12 · 2026-03-28 00:28:55

86

Views

A question about Exercise 2.11 from Atiyah's "Introduction to Commutative Algebra"

Published on 28 Mar 2026 - 0:28

score 183 · Answer 13 · 2026-03-28 16:19:59

183

Views

Unique representation of a graph (graph automorphism) in python

Published on 28 Mar 2026 - 16:19

score 234 · Answer 14 · 2026-03-28 12:32:08

234

Views

Does there exist a group $G$, such that $G\otimes H \cong G$ for all finite groups, $H$?

Published on 28 Mar 2026 - 12:32

score 55 · Answer 15 · 2022-12-13 05:54:39

55

Views

How to prove that $\mathbb{C}^\times \not\simeq \mathbb{R}^\times \times S^1$.

Published on 13 Dec 2022 - 5:54

List Question

Let $G=\mathbb{Z}\big /4\mathbb{Z}$ and $H=2\mathbb{Z}\big /4\mathbb{Z}$. Is $H$ isomorphic to $G\big / H$?

Inclusion induces homology group isomorphism

Why $E/AutE$ is isomorphic to $\Bbb{P}^1$?

Why are there only 5 abelian groups of order 48?

Show $\phi : S_3 \rightarrow S_3$ given by $\phi(f^{i}g^{j}) = f^{2i}g^{j}$ is an automorphism

Show $A_5 \cong \langle x,y \mid x^5,y^2,(xy)^3\rangle$

Understanding butterfly lemma and Isomorphism theorems

Prove that $[K : aHa^{-1} \cap K]$ is equal to number of left cosets of $H$ in $KaH$, where $K, H$ are subgroups of $G$ and $a\in G$

Is the number of homomorphisms between two isomorphic groups equals to the number of Automorphisms for each group?

Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Find all homomorphisms from $(\mathbb{Z}_8,+)$ into $(\mathbb{Z}_6,+)$.

A question about Exercise 2.11 from Atiyah's "Introduction to Commutative Algebra"

Unique representation of a graph (graph automorphism) in python

Does there exist a group $G$, such that $G\otimes H \cong G$ for all finite groups, $H$?

How to prove that $\mathbb{C}^\times \not\simeq \mathbb{R}^\times \times S^1$.

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