Question

Show that if $G$ is a group of order $168$ that has a normal subgroup of order $4$ , then $G$ has a normal subgroup of order $28$

score 3.1k · Answer 1 · 2026-03-26 23:10:41

3.1k

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Show that if $G$ is a group of order $168$ that has a normal subgroup of order $4$ , then $G$ has a normal subgroup of order $28$

Published on 26 Mar 2026 - 23:10

score 3.5k · Answer 2 · 2026-03-26 23:10:36

3.5k

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If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

Published on 26 Mar 2026 - 23:10

score 288 · Answer 3 · 2014-08-27 23:08:29

288

Views

Cardinality of $\text{Aut}(G\times G) $

Published on 27 Aug 2014 - 23:08

score 70 · Answer 4 · 2026-04-03 13:40:02

70

Views

Help explain linear algebra/differential calculus theorem in simpler terms.

Published on 03 Apr 2026 - 13:40

score 537 · Answer 5 · 2026-03-26 21:27:09

537

Views

Number of non isomorphic groups of order $122$, My attempt through Sylow theory.

Published on 26 Mar 2026 - 21:27

score 449 · Answer 6 · 2014-08-28 18:55:22

449

Views

Left regular representation of a group through group action

Published on 28 Aug 2014 - 18:55

score 92 · Answer 7 · 2014-08-28 21:19:22

92

Views

Finding commutator of $\mathbb D_n$ and $\mathbb S_4$

Published on 28 Aug 2014 - 21:19

score 104 · Answer 8 · 2026-03-28 13:30:57

104

Views

Proving certain groups are normal

Published on 28 Mar 2026 - 13:30

score 831 · Answer 9 · 2026-03-26 12:53:50

831

Views

Alternative way of proving the subgroup of rotations is normal in $\mathbb D_4$

Published on 26 Mar 2026 - 12:53

score 115 · Answer 10 · 2026-03-28 12:02:33

115

Views

Calculate quotients of $\mathbb S_3$ and $\mathbb D_4$

Published on 28 Mar 2026 - 12:02

score 191 · Answer 11 · 2026-03-25 23:35:47

191

Views

Software or tool for investigating groups

Published on 25 Mar 2026 - 23:35

score 905 · Answer 12 · 2026-03-26 21:27:22

905

Views

A group of order $120$ has a subgroup of index $3$ or $5$ (or both)

Published on 26 Mar 2026 - 21:27

score 1.4k · Answer 13 · 2026-03-25 07:44:58

1.4k

Views

Is every finite group of isometries a subgroup of a finite reflection group?

Published on 25 Mar 2026 - 7:44

score 116 · Answer 14 · 2014-08-30 00:15:41

116

Views

Is a primitive permutation group, indecomposable?

Published on 30 Aug 2014 - 0:15

score 197 · Answer 15 · 2014-08-30 17:09:22

197

Views

Classification of the decomposable primitive permutation groups

Published on 30 Aug 2014 - 17:09

List Question

Show that if $G$ is a group of order $168$ that has a normal subgroup of order $4$ , then $G$ has a normal subgroup of order $28$

If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

Cardinality of $\text{Aut}(G\times G) $

Help explain linear algebra/differential calculus theorem in simpler terms.

Number of non isomorphic groups of order $122$, My attempt through Sylow theory.

Left regular representation of a group through group action

Finding commutator of $\mathbb D_n$ and $\mathbb S_4$

Proving certain groups are normal

Alternative way of proving the subgroup of rotations is normal in $\mathbb D_4$

Calculate quotients of $\mathbb S_3$ and $\mathbb D_4$

Software or tool for investigating groups

A group of order $120$ has a subgroup of index $3$ or $5$ (or both)

Is every finite group of isometries a subgroup of a finite reflection group?

Is a primitive permutation group, indecomposable?

Classification of the decomposable primitive permutation groups

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