Question

If $H_i \unlhd H_{i+1}$ and $N$ is simple then $H_iN \unlhd H_{i+1} N$

score 30 · Answer 1 · 2026-03-26 08:02:28

30

Views

If $H_i \unlhd H_{i+1}$ and $N$ is simple then $H_iN \unlhd H_{i+1} N$

Published on 26 Mar 2026 - 8:02

score 1k · Answer 2 · 2026-03-29 23:48:13

1k

Views

Symmetric group $\mathfrak{S}_4$ does not have a normal subgroup of order 2.

Published on 29 Mar 2026 - 23:48

score 180 · Answer 3 · 2016-08-22 21:35:28

180

Views

For a subgroups $H_1$ and $H_2$ of $G$ and a normal subgroup $N$ of $G$: $H_1/N \cong H_2/N \Rightarrow H_1 \cong H_2$. Is it true?

Published on 22 Aug 2016 - 21:35

score 407 · Answer 4 · 2026-03-26 17:32:15

407

Views

A characteristic subgroup of the free group $F_2$

Published on 26 Mar 2026 - 17:32

score 1000 · Answer 5 · 2026-03-26 17:42:26

1000

Views

$G$ be a group with subgroups $H,K$ such that $G=HK$ , $|H \cap K|=1$ and $H$ is normal in $G$ , then is $K$ also normal in $G$?

Published on 26 Mar 2026 - 17:42

score 394 · Answer 6 · 2016-08-30 14:41:48

394

Views

Implication in Zassenhaus Lemma

Published on 30 Aug 2016 - 14:41

score 238 · Answer 7 · 2026-03-26 06:31:44

238

Views

$H$ is a normal subgroup (containing an element of infinite order) of the permutation group over positive integers , then is $H$ the whole group?

Published on 26 Mar 2026 - 6:31

score 2.8k · Answer 8 · 2016-09-03 12:55:33

2.8k

Views

If $H$ and $K$ are abelian normal subgroups of a group that intersect trivially, then prove $HK$ is abelian.

Published on 03 Sep 2016 - 12:55

score 466 · Answer 9 · 2016-09-03 20:59:03

466

Views

Generating a subgroup with two permutations

Published on 03 Sep 2016 - 20:59

score 110 · Answer 10 · 2016-09-04 19:37:29

110

Views

Quotient Groups: relating properties of H to properties of G/H

Published on 04 Sep 2016 - 19:37

score 118 · Answer 11 · 2016-09-07 20:41:12

118

Views

Determining Why X is a Subgroup of Y

Published on 07 Sep 2016 - 20:41

score 56 · Answer 12 · 2026-03-30 06:32:41

56

Views

For G acting on $\Omega$, let $\alpha \in \Omega$, show that $\operatorname{Stab}_G(\alpha) \vartriangleleft G$

Published on 30 Mar 2026 - 6:32

score 64 · Answer 13 · 2026-03-26 08:02:22

64

Views

Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

Published on 26 Mar 2026 - 8:02

score 447 · Answer 14 · 2026-03-29 04:11:40

447

Views

Is any subgroup normal?

Published on 29 Mar 2026 - 4:11

score 741 · Answer 15 · 2026-03-29 05:44:09

741

Views

How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

Published on 29 Mar 2026 - 5:44

List Question

If $H_i \unlhd H_{i+1}$ and $N$ is simple then $H_iN \unlhd H_{i+1} N$

Symmetric group $\mathfrak{S}_4$ does not have a normal subgroup of order 2.

For a subgroups $H_1$ and $H_2$ of $G$ and a normal subgroup $N$ of $G$: $H_1/N \cong H_2/N \Rightarrow H_1 \cong H_2$. Is it true?

A characteristic subgroup of the free group $F_2$

$G$ be a group with subgroups $H,K$ such that $G=HK$ , $|H \cap K|=1$ and $H$ is normal in $G$ , then is $K$ also normal in $G$?

Implication in Zassenhaus Lemma

$H$ is a normal subgroup (containing an element of infinite order) of the permutation group over positive integers , then is $H$ the whole group?

If $H$ and $K$ are abelian normal subgroups of a group that intersect trivially, then prove $HK$ is abelian.

Generating a subgroup with two permutations

Quotient Groups: relating properties of H to properties of G/H

Determining Why X is a Subgroup of Y

For G acting on $\Omega$, let $\alpha \in \Omega$, show that $\operatorname{Stab}_G(\alpha) \vartriangleleft G$

Let G be simple, |G| is not 2, and ϕ a homomorphism from G to H. If H contains a normal subgroup A of index 2, then ϕ(G) ≤ A .

Is any subgroup normal?

How to apply 1st Isomorphism Theorem to show that a finite abelian group has a subgroup of order $n$ for each positive divisor $n$ of its order

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