Question

If $G$ is a group of finite order and $p$ is a prime, then $N\triangleleft G,\ H\leq G,\ |G/N|=p\Longrightarrow H\subset N$ or $NH= G$.

score 107 · Answer 1 · 2021-06-20 01:29:27

107

Views

If $G$ is a group of finite order and $p$ is a prime, then $N\triangleleft G,\ H\leq G,\ |G/N|=p\Longrightarrow H\subset N$ or $NH= G$.

Published on 20 Jun 2021 - 1:29

score 272 · Answer 2 · 2021-06-20 07:15:51

272

Views

The converse: If $G$ is abelian and if $N\le G$, prove that $G/N$ is abelian

Published on 20 Jun 2021 - 7:15

score 167 · Answer 3 · 2021-06-21 20:50:05

167

Views

The Kernel in the First Isomorphism Theorem

Published on 21 Jun 2021 - 20:50

score 202 · Answer 4 · 2021-06-25 03:40:45

202

Views

Subgroups of Quotient group $\Bbb Q/\Bbb Z$ of infinite order .

Published on 25 Jun 2021 - 3:40

score 156 · Answer 5 · 2026-03-28 02:04:55

156

Views

Quotient of $\mathbb{R^*}$ by cyclic group product

Published on 28 Mar 2026 - 2:04

score 334 · Answer 6 · 2026-03-28 11:54:04

334

Views

Let $G$ be a group and $H\unlhd G$. Prove that if $G/H$ is a simple group, then $G\neq H$ and $\not\exists K$ s.t. $H\leq K\leq G,K \unlhd G.$

Published on 28 Mar 2026 - 11:54

score 110 · Answer 7 · 2021-06-28 05:09:45

110

Views

Proving that $3\mathbb{Z}/6\mathbb{Z} \trianglelefteq \mathbb{Z}/6\mathbb{Z}$.

Published on 28 Jun 2021 - 5:09

score 255 · Answer 8 · 2021-07-04 00:21:17

255

Views

Why is $S_3 / A_3$ cyclic group of order $2$?

Published on 04 Jul 2021 - 0:21

score 147 · Answer 9 · 2021-07-16 18:19:21

147

Views

Showing that the rank of $(G/H)/(G/H)_t$ is $n - m$

Published on 16 Jul 2021 - 18:19

score 59 · Answer 10 · 2021-07-16 22:20:02

59

Views

If $[G:mG]$ is finite, where $m>1$ and $G$ is infinite abelian, under what conditions does $[G:mG]$ divide $m$?

Published on 16 Jul 2021 - 22:20

score 201 · Answer 11 · 2021-07-17 18:27:34

201

Views

An abelian group has Prüfer rank at most one iff it is isomorphic to a subgroup of either $\Bbb Q$ or $\Bbb Q/\Bbb Z$.

Published on 17 Jul 2021 - 18:27

score 171 · Answer 12 · 2021-07-21 16:21:05

171

Views

Is $SU(n)/\mathbb Z_n$ a Lie group?

Published on 21 Jul 2021 - 16:21

score 94 · Answer 13 · 2026-03-28 02:06:35

94

Views

For $H\le G$, abelian $G$, show that $r_0(H)+r_0(G/H)=r_0(G)$, where $r_0(K)$ is the torsionfree rank of $K$

Published on 28 Mar 2026 - 2:06

score 95 · Answer 14 · 2021-07-24 08:25:18

95

Views

Description of $S_4/H$ as a set where $H$ is order $8$ subgroup of $S_4$

Published on 24 Jul 2021 - 8:25

score 116 · Answer 15 · 2026-03-25 07:46:27

116

Views

How does the nth Symmetric Power result from the quotient of the group of rank N tensors?

Published on 25 Mar 2026 - 7:46

List Question

If $G$ is a group of finite order and $p$ is a prime, then $N\triangleleft G,\ H\leq G,\ |G/N|=p\Longrightarrow H\subset N$ or $NH= G$.

The converse: If $G$ is abelian and if $N\le G$, prove that $G/N$ is abelian

The Kernel in the First Isomorphism Theorem

Subgroups of Quotient group $\Bbb Q/\Bbb Z$ of infinite order .

Quotient of $\mathbb{R^*}$ by cyclic group product

Let $G$ be a group and $H\unlhd G$. Prove that if $G/H$ is a simple group, then $G\neq H$ and $\not\exists K$ s.t. $H\leq K\leq G,K \unlhd G.$

Proving that $3\mathbb{Z}/6\mathbb{Z} \trianglelefteq \mathbb{Z}/6\mathbb{Z}$.

Why is $S_3 / A_3$ cyclic group of order $2$?

Showing that the rank of $(G/H)/(G/H)_t$ is $n - m$

If $[G:mG]$ is finite, where $m>1$ and $G$ is infinite abelian, under what conditions does $[G:mG]$ divide $m$?

An abelian group has Prüfer rank at most one iff it is isomorphic to a subgroup of either $\Bbb Q$ or $\Bbb Q/\Bbb Z$.

Is $SU(n)/\mathbb Z_n$ a Lie group?

For $H\le G$, abelian $G$, show that $r_0(H)+r_0(G/H)=r_0(G)$, where $r_0(K)$ is the torsionfree rank of $K$

Description of $S_4/H$ as a set where $H$ is order $8$ subgroup of $S_4$

How does the nth Symmetric Power result from the quotient of the group of rank N tensors?

Trending Questions

Popular # Hahtags

Popular Questions