Question

If $N \trianglelefteq G$ then $(gN)^\alpha = g^\alpha N$ for $\alpha \in \mathbb{Z}$.

score 378 · Answer 1 · 2026-03-30 23:12:41

378

Views

If $N \trianglelefteq G$ then $(gN)^\alpha = g^\alpha N$ for $\alpha \in \mathbb{Z}$.

Published on 30 Mar 2026 - 23:12

score 1.4k · Answer 2 · 2015-03-08 19:12:04

1.4k

Views

Quotient group with multiplication table involving the Klein 4 subgroup.

Published on 08 Mar 2015 - 19:12

score 1.3k · Answer 3 · 2015-03-09 10:48:21

1.3k

Views

If $H$ is a normal subgroup of $G$, prove $g^{n} \in H$

Published on 09 Mar 2015 - 10:48

score 94 · Answer 4 · 2026-03-30 23:15:31

94

Views

Let $H,K$ be finite groups , if for any finite group $G$ , $h(G,K)=h(G,H)$ holds , then is it true that $i(G,H)=i(G,K)$ for any finite group $G$ ?

Published on 30 Mar 2026 - 23:15

score 136 · Answer 5 · 2015-03-14 13:16:15

136

Views

Problem about the subgroup generated by the commutators.

Published on 14 Mar 2015 - 13:16

score 47 · Answer 6 · 2015-03-16 07:29:42

47

Views

Is it a coincidence that $\mathbb{Z_{12}}$ has all distinct subgroups that are factors of 12?

Published on 16 Mar 2015 - 7:29

score 216 · Answer 7 · 2026-03-27 14:02:26

216

Views

Number of normal subgroups from $F_{2}$ which factor groups are isomorphic to $D_{n}$

Published on 27 Mar 2026 - 14:02

score 162 · Answer 8 · 2015-03-18 19:38:38

162

Views

proof: every $g \in G$ can be written as $g =nm$

Published on 18 Mar 2015 - 19:38

score 266 · Answer 9 · 2026-03-26 07:58:57

266

Views

Prove: $G = HN$, and $H \cap N =$ {$e$}, (Isometries in $\mathbb{R^2}$)

Published on 26 Mar 2026 - 7:58

score 2.5k · Answer 10 · 2015-03-21 20:45:09

2.5k

Views

Prove H is a normal subgroup of G.

Published on 21 Mar 2015 - 20:45

score 237 · Answer 11 · 2015-03-23 23:26:54

237

Views

Find the number of normal subgroups of $A_4$.

Published on 23 Mar 2015 - 23:26

score 725 · Answer 12 · 2015-03-26 04:43:49

725

Views

Show that H is normal subgroup of G.

Published on 26 Mar 2015 - 4:43

score 58 · Answer 13 · 2015-03-30 09:55:57

58

Views

Prove: $G \cong M \times N$ and $G$ is finite $\Rightarrow order(N)$ is not divisible by 5

Published on 30 Mar 2015 - 9:55

score 40 · Answer 14 · 2015-04-01 02:48:42

40

Views

Naively showing that $A_n$ mod a nontrivial normal subgroup is abelian.

Published on 01 Apr 2015 - 2:48

score 580 · Answer 15 · 2026-02-23 05:37:51

580

Views

All characteristic subgroups are normal

Published on 23 Feb 2026 - 5:37

List Question

If $N \trianglelefteq G$ then $(gN)^\alpha = g^\alpha N$ for $\alpha \in \mathbb{Z}$.

Quotient group with multiplication table involving the Klein 4 subgroup.

If $H$ is a normal subgroup of $G$, prove $g^{n} \in H$

Let $H,K$ be finite groups , if for any finite group $G$ , $h(G,K)=h(G,H)$ holds , then is it true that $i(G,H)=i(G,K)$ for any finite group $G$ ?

Problem about the subgroup generated by the commutators.

Is it a coincidence that $\mathbb{Z_{12}}$ has all distinct subgroups that are factors of 12?

Number of normal subgroups from $F_{2}$ which factor groups are isomorphic to $D_{n}$

proof: every $g \in G$ can be written as $g =nm$

Prove: $G = HN$, and $H \cap N =$ {$e$}, (Isometries in $\mathbb{R^2}$)

Prove H is a normal subgroup of G.

Find the number of normal subgroups of $A_4$.

Show that H is normal subgroup of G.

Prove: $G \cong M \times N$ and $G$ is finite $\Rightarrow order(N)$ is not divisible by 5

Naively showing that $A_n$ mod a nontrivial normal subgroup is abelian.

All characteristic subgroups are normal

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