Question

Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.

score 193 · Answer 1 · 2026-04-26 21:05:38

193

Views

Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.

Published on 26 Apr 2026 - 21:05

score 44 · Answer 2 · 2026-04-17 12:59:00

44

Views

Isomorphism of 2 algebras with 1

Published on 17 Apr 2026 - 12:59

score 39 · Answer 3 · 2026-04-13 02:14:14

39

Views

Then find the polynomial $ \ f \ $ for which $ \ H(f)=0 \ $

Published on 13 Apr 2026 - 2:14

score 177 · Answer 4 · 2026-04-14 15:11:29

177

Views

Addition and multiplication are one and the same.....can this be generalized to any operators????

Published on 14 Apr 2026 - 15:11

score 5.5k · Answer 5 · 2026-04-10 11:22:59

5.5k

Views

If $G$ has exactly one subgroup $H$ of order $k$, prove that $H$ is normal in $G$.

Published on 10 Apr 2026 - 11:22

score 183 · Answer 6 · 2026-04-24 00:53:23

183

Views

What is this group $G=\langle a,b,c\mid a^2=1, b^2=1, c^2=ab\rangle$

Published on 24 Apr 2026 - 0:53

score 94 · Answer 7 · 2026-04-09 17:28:05

94

Views

A question about normalizer

Published on 09 Apr 2026 - 17:28

score 1.7k · Answer 8 · 2026-04-13 02:50:46

1.7k

Views

Defining tensor transpose without representing them as matrices

Published on 13 Apr 2026 - 2:50

score 101 · Answer 9 · 2026-04-14 23:55:00

101

Views

Ring homomorphism $\mathbb{Z}[[t]]\otimes_\mathbb{Z} \mathbb{Q}\rightarrow \mathbb{Q}[[t]]$

Published on 14 Apr 2026 - 23:55

score 21 · Answer 10 · 2026-04-16 13:24:42

21

Views

Is this an equivalent definition of the notation $f(x) \equiv g(x) \hspace{4mm} ( \text{mod} \hspace{2mm} h(x), \hspace{1mm} n )$?

Published on 16 Apr 2026 - 13:24

score 44 · Answer 11 · 2026-04-09 12:02:22

44

Views

Can $A[[X]]$ be a finitely generated $A$-algebra?

Published on 09 Apr 2026 - 12:02

score 137 · Answer 12 · 2026-04-22 12:51:32

137

Views

Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Published on 22 Apr 2026 - 12:51

score 326 · Answer 13 · 2026-04-14 12:54:25

326

Views

Fundamental Theorem of Abelian Groups - intuition regarding Lemma

Published on 14 Apr 2026 - 12:54

score 278 · Answer 14 · 2026-04-13 09:52:50

278

Views

Is there an algorithm/method for actually drawing Van Kampen diagrams?

Published on 13 Apr 2026 - 9:52

score 99 · Answer 15 · 2026-04-12 13:02:57

99

Views

Splitting fields isomorphic

Published on 12 Apr 2026 - 13:02

List Question

Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.

Isomorphism of 2 algebras with 1

Then find the polynomial $ \ f \ $ for which $ \ H(f)=0 \ $

Addition and multiplication are one and the same.....can this be generalized to any operators????

If $G$ has exactly one subgroup $H$ of order $k$, prove that $H$ is normal in $G$.

What is this group $G=\langle a,b,c\mid a^2=1, b^2=1, c^2=ab\rangle$

A question about normalizer

Defining tensor transpose without representing them as matrices

Ring homomorphism $\mathbb{Z}[[t]]\otimes_\mathbb{Z} \mathbb{Q}\rightarrow \mathbb{Q}[[t]]$

Is this an equivalent definition of the notation $f(x) \equiv g(x) \hspace{4mm} ( \text{mod} \hspace{2mm} h(x), \hspace{1mm} n )$?

Can $A[[X]]$ be a finitely generated $A$-algebra?

Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Fundamental Theorem of Abelian Groups - intuition regarding Lemma

Is there an algorithm/method for actually drawing Van Kampen diagrams?

Splitting fields isomorphic

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