Question

If there is subgroup of finite index $n$ and $G$ is finitely generated then there is a subgroup of $G$ that has index $n$ and is characteristic in $G$

score 111 · Answer 1 · 2026-03-30 06:42:57

111

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If there is subgroup of finite index $n$ and $G$ is finitely generated then there is a subgroup of $G$ that has index $n$ and is characteristic in $G$

Published on 30 Mar 2026 - 6:42

score 295 · Answer 2 · 2026-03-29 17:26:52

295

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Exercise 9, Section 2.5 of Hungerford’s Abstract Algebra

Published on 29 Mar 2026 - 17:26

score 60 · Answer 3 · 2026-03-27 04:14:59

60

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Are commutator subgroups simple?

Published on 27 Mar 2026 - 4:14

score 253 · Answer 4 · 2026-04-01 01:06:30

253

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Show that a subgroup of order $3$ is normal in a group of order $15$

Published on 01 Apr 2026 - 1:06

score 377 · Answer 5 · 2026-03-28 03:27:45

377

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Is it possible for a normal subgroup of a finite group have greater number of elements in the minimal generating set?

Published on 28 Mar 2026 - 3:27

score 231 · Answer 6 · 2026-03-29 07:40:27

231

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Let $S\subseteq G$ for a group $G$. What is the relationship between $\langle S\rangle_G$ and ${\rm ncl}_G(S)$?

Published on 29 Mar 2026 - 7:40

score 240 · Answer 7 · 2023-11-13 20:27:41

240

Views

Prove that any subgroup of $G$ containing a special subgroup of $G$ is also special.

Published on 13 Nov 2023 - 20:27

score 40 · Answer 8 · 2026-03-26 22:13:51

40

Views

Clarification over subnormal series of a group

Published on 26 Mar 2026 - 22:13

score 145 · Answer 9 · 2026-03-27 00:04:03

145

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The group $S_7$ has no subgroups of order $840$.

Published on 27 Mar 2026 - 0:04

score 142 · Answer 10 · 2026-03-29 16:00:51

142

Views

Let $p$ and $q$ be twin primes, both greater than or equal to $5$ , is every group of order $p^2q^2$ abelian?

Published on 29 Mar 2026 - 16:00

score 125 · Answer 11 · 2026-03-27 00:10:24

125

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$n\ge 5$, prove $A_n$ is the only non-trivial proper normal subgroup of $S_n$.

Published on 27 Mar 2026 - 0:10

score 48 · Answer 12 · 2023-11-23 10:46:07

48

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For a normal subgroup $H$ of $G$. how to prove $XH=HX$ for any part of $G$ ? Is union distributive over multiplication?

Published on 23 Nov 2023 - 10:46

score 75 · Answer 13 · 2023-11-27 02:44:20

75

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Normal subgroup of $S_9$

Published on 27 Nov 2023 - 2:44

score 56 · Answer 14 · 2023-11-29 01:02:22

56

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Typo? "If $G$ is a group, $H$ and $K$ are subgroups of $G$, and $K\unlhd G$. Is $H\cap K \unlhd H$ just if $K \subset H$?"

Published on 29 Nov 2023 - 1:02

score 153 · Answer 15 · 2026-03-27 01:00:08

153

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When are all normal subgroups of a direct product of finite groups a direct product of normal subgroups?

Published on 27 Mar 2026 - 1:00

List Question

If there is subgroup of finite index $n$ and $G$ is finitely generated then there is a subgroup of $G$ that has index $n$ and is characteristic in $G$

Exercise 9, Section 2.5 of Hungerford’s Abstract Algebra

Are commutator subgroups simple?

Show that a subgroup of order $3$ is normal in a group of order $15$

Is it possible for a normal subgroup of a finite group have greater number of elements in the minimal generating set?

Let $S\subseteq G$ for a group $G$. What is the relationship between $\langle S\rangle_G$ and ${\rm ncl}_G(S)$?

Prove that any subgroup of $G$ containing a special subgroup of $G$ is also special.

Clarification over subnormal series of a group

The group $S_7$ has no subgroups of order $840$.

Let $p$ and $q$ be twin primes, both greater than or equal to $5$ , is every group of order $p^2q^2$ abelian?

$n\ge 5$, prove $A_n$ is the only non-trivial proper normal subgroup of $S_n$.

For a normal subgroup $H$ of $G$. how to prove $XH=HX$ for any part of $G$ ? Is union distributive over multiplication?

Normal subgroup of $S_9$

Typo? "If $G$ is a group, $H$ and $K$ are subgroups of $G$, and $K\unlhd G$. Is $H\cap K \unlhd H$ just if $K \subset H$?"

When are all normal subgroups of a direct product of finite groups a direct product of normal subgroups?

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