Question

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

score 75 · Answer 1 · 2026-04-13 16:39:36

75

Views

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

Published on 13 Apr 2026 - 16:39

score 853 · Answer 2 · 2026-04-12 15:05:20

853

Views

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

Published on 12 Apr 2026 - 15:05

score 49 · Answer 3 · 2026-04-13 06:12:47

49

Views

dφ is bijective but φ is not a lie group isomorphism

Published on 13 Apr 2026 - 6:12

score 79 · Answer 4 · 2026-04-15 09:13:01

79

Views

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

Published on 15 Apr 2026 - 9:13

score 272 · Answer 5 · 2026-04-12 20:13:01

272

Views

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

Published on 12 Apr 2026 - 20:13

score 54 · Answer 6 · 2026-05-11 09:33:36

54

Views

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

Published on 11 May 2026 - 9:33

score 124 · Answer 7 · 2026-04-09 15:06:03

124

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 09 Apr 2026 - 15:06

score 336 · Answer 8 · 2026-04-16 03:44:06

336

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 2026 - 3:44

score 46 · Answer 9 · 2026-04-08 18:21:36

46

Views

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

Published on 08 Apr 2026 - 18:21

score 79 · Answer 10 · 2026-05-10 19:03:29

79

Views

Isomorphism problem for the center of modular group algebras

Published on 10 May 2026 - 19:03

score 147 · Answer 11 · 2026-04-15 02:43:47

147

Views

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

Published on 15 Apr 2026 - 2:43

score 107 · Answer 12 · 2026-04-14 18:19:50

107

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 14 Apr 2026 - 18:19

score 834 · Answer 13 · 2026-05-11 02:52:35

834

Views

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

Published on 11 May 2026 - 2:52

score 357 · Answer 14 · 2026-04-10 19:26:00

357

Views

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

Published on 10 Apr 2026 - 19:26

score 133 · Answer 15 · 2026-05-11 00:23:05

133

Views

Isomorphism factor by factor

Published on 11 May 2026 - 0:23

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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