Question

Step in proof of "Does $G\times K\cong H\times K$ imply $G\cong H$?"

score 72 · Answer 1 · 2019-04-06 14:18:43

72

Views

Step in proof of "Does $G\times K\cong H\times K$ imply $G\cong H$?"

Published on 06 Apr 2019 - 14:18

score 850 · Answer 2 · 2019-04-08 17:44:23

850

Views

What's an isomorphism between $Z_{p^2}^*$ and $Z_p\times Z_{p-1}$

Published on 08 Apr 2019 - 17:44

score 47 · Answer 3 · 2026-03-29 17:24:37

47

Views

dφ is bijective but φ is not a lie group isomorphism

Published on 29 Mar 2026 - 17:24

score 76 · Answer 4 · 2019-04-10 07:51:37

76

Views

Find subgroup of $GL(n,\mathbb{Z}_{19})$ with index 3

Published on 10 Apr 2019 - 7:51

score 269 · Answer 5 · 2019-04-13 04:09:14

269

Views

Proving the given $\mathbb R^3/H$ $\cong$ $\mathbb R^2$ where $H$ = {$(y,0,0)|y \in \mathbb R$}

Published on 13 Apr 2019 - 4:09

score 51 · Answer 6 · 2026-03-25 19:05:30

51

Views

If $(m, n) = 1$, then $\dfrac{\mathbb Z \times \mathbb Z}{\langle (m,n)\rangle}\cong\mathbb Z$

Published on 25 Mar 2026 - 19:05

score 122 · Answer 7 · 2026-03-26 22:16:22

122

Views

Mapping from $\mathbb Z/2\mathbb Z \times \mathbb Z/3\mathbb Z \times \dots\times \mathbb Z/p_n\mathbb Z$ to $\mathbb Z/p_n\#\mathbb Z$.

Published on 26 Mar 2026 - 22:16

score 333 · Answer 8 · 2019-04-16 10:22:40

333

Views

Prove that subgroup of all elements of finite order in group $(\mathbb{C} \setminus \{0\}, \cdot)$ is isomorphic to $\mathbb{Q}/\mathbb{Z}$

Published on 16 Apr 2019 - 10:22

score 43 · Answer 9 · 2019-04-16 16:18:32

43

Views

How do I find the kernel of a given group homomorphism?

Published on 16 Apr 2019 - 16:18

score 76 · Answer 10 · 2026-03-25 11:02:24

76

Views

Isomorphism problem for the center of modular group algebras

Published on 25 Mar 2026 - 11:02

score 145 · Answer 11 · 2026-03-26 21:27:10

145

Views

Is there any injective homomorphism (i.e. monomorphism) from a non-cyclic group of order $4$ to $\mathbb{Z}_8$?

Published on 26 Mar 2026 - 21:27

score 104 · Answer 12 · 2019-04-17 20:06:50

104

Views

Let $A_1$, $A_2$ be groups and $\phi:A_1\to A_2$ surjective with $G_1\unlhd A_1$ and $\phi(G_1)=G_2$. Is $A_1/G_1\cong A_2/G_2$?

Published on 17 Apr 2019 - 20:06

score 831 · Answer 13 · 2026-03-26 04:31:10

831

Views

Is $D_n$ isomorphic to $C_n \times C_2$?

Published on 26 Mar 2026 - 4:31

score 354 · Answer 14 · 2019-04-19 05:31:58

354

Views

Given $H \leq G$, prove isomorphism of $H$ and $gHg^{-1}$

Published on 19 Apr 2019 - 5:31

score 127 · Answer 15 · 2026-03-25 09:22:20

127

Views

Isomorphism factor by factor

Published on 25 Mar 2026 - 9:22

List Question

Step in proof of "Does $G\times K\cong H\times K$ imply $G\cong H$?"

What's an isomorphism between $Z_{p^2}^*$ and $Z_p\times Z_{p-1}$

dφ is bijective but φ is not a lie group isomorphism

Find subgroup of $GL(n,\mathbb{Z}_{19})$ with index 3

Proving the given $\mathbb R^3/H$ $\cong$ $\mathbb R^2$ where $H$ = {$(y,0,0)|y \in \mathbb R$}

If $(m, n) = 1$, then $\dfrac{\mathbb Z \times \mathbb Z}{\langle (m,n)\rangle}\cong\mathbb Z$

Mapping from $\mathbb Z/2\mathbb Z \times \mathbb Z/3\mathbb Z \times \dots\times \mathbb Z/p_n\mathbb Z$ to $\mathbb Z/p_n\#\mathbb Z$.

Prove that subgroup of all elements of finite order in group $(\mathbb{C} \setminus \{0\}, \cdot)$ is isomorphic to $\mathbb{Q}/\mathbb{Z}$

How do I find the kernel of a given group homomorphism?

Isomorphism problem for the center of modular group algebras

Is there any injective homomorphism (i.e. monomorphism) from a non-cyclic group of order $4$ to $\mathbb{Z}_8$?

Let $A_1$, $A_2$ be groups and $\phi:A_1\to A_2$ surjective with $G_1\unlhd A_1$ and $\phi(G_1)=G_2$. Is $A_1/G_1\cong A_2/G_2$?

Is $D_n$ isomorphic to $C_n \times C_2$?

Given $H \leq G$, prove isomorphism of $H$ and $gHg^{-1}$

Isomorphism factor by factor

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