Question

Index of a common normal core

score 98 · Answer 1 · 2026-03-25 01:22:25

98

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Index of a common normal core

Published on 25 Mar 2026 - 1:22

score 51 · Answer 2 · 2018-12-20 00:07:03

51

Views

Connected normal compact subgroups of $GL \left(2, \mathbb{C} \right)$

Published on 20 Dec 2018 - 0:07

score 1.2k · Answer 3 · 2018-12-22 00:50:41

1.2k

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Intersection of a Family of Normal Subgroups of a Group G is also a Normal Subgroup of G

Published on 22 Dec 2018 - 0:50

score 52 · Answer 4 · 2018-12-24 04:20:31

52

Views

Show that $(M\times N)/R\cong M$.

Published on 24 Dec 2018 - 4:20

score 144 · Answer 5 · 2018-12-26 18:26:59

144

Views

Does normality of a subgroup imply it has index 2?

Published on 26 Dec 2018 - 18:26

score 589 · Answer 6 · 2026-03-26 11:17:55

589

Views

Is there exist a group homomorphism from the symmetric group $S_n$ to $S_{n-1}$ for $n \ge 5?$

Published on 26 Mar 2026 - 11:17

score 116 · Answer 7 · 2026-03-26 12:53:30

116

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Let $N$ be an Abelian normal subgroup of $G$, if $G/N$ is perfect, then also $G'$ is perfect.

Published on 26 Mar 2026 - 12:53

score 638 · Answer 8 · 2026-03-25 14:35:54

638

Views

Given that $G/H=\{xH:x \in G\}$ is group under operation $(xH)(yH)=(xyH)$ . Then $H$ is normal subgroup of $G$

Published on 25 Mar 2026 - 14:35

score 252 · Answer 9 · 2026-03-25 04:43:36

252

Views

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

Published on 25 Mar 2026 - 4:43

score 103 · Answer 10 · 2026-03-26 09:49:37

103

Views

How is it possible that $\textrm{HK}=\textrm{G}$?

Published on 26 Mar 2026 - 9:49

score 98 · Answer 11 · 2026-03-25 23:39:14

98

Views

If $G$ has a nontrivial centre, must every subgroup of index $3$ be normal?

Published on 25 Mar 2026 - 23:39

score 114 · Answer 12 · 2026-03-25 14:36:49

114

Views

Is G/H a group even if H is a subgroup of G but not a normal subgroup?

Published on 25 Mar 2026 - 14:36

score 216 · Answer 13 · 2026-03-25 08:07:39

216

Views

Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Published on 25 Mar 2026 - 8:07

score 1.1k · Answer 14 · 2026-03-25 14:47:05

1.1k

Views

Are normal subgroups of a profinite group with finite index closed?

Published on 25 Mar 2026 - 14:47

score 83 · Answer 15 · 2026-03-25 16:06:34

83

Views

project normal subgroup generated by a subgroup to its abelianization

Published on 25 Mar 2026 - 16:06

List Question

Index of a common normal core

Connected normal compact subgroups of $GL \left(2, \mathbb{C} \right)$

Intersection of a Family of Normal Subgroups of a Group G is also a Normal Subgroup of G

Show that $(M\times N)/R\cong M$.

Does normality of a subgroup imply it has index 2?

Is there exist a group homomorphism from the symmetric group $S_n$ to $S_{n-1}$ for $n \ge 5?$

Let $N$ be an Abelian normal subgroup of $G$, if $G/N$ is perfect, then also $G'$ is perfect.

Given that $G/H=\{xH:x \in G\}$ is group under operation $(xH)(yH)=(xyH)$ . Then $H$ is normal subgroup of $G$

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

How is it possible that $\textrm{HK}=\textrm{G}$?

If $G$ has a nontrivial centre, must every subgroup of index $3$ be normal?

Is G/H a group even if H is a subgroup of G but not a normal subgroup?

Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Are normal subgroups of a profinite group with finite index closed?

project normal subgroup generated by a subgroup to its abelianization

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