Question

Kernel is a normal subgroup of the preimage

score 202 · Answer 1 · 2026-03-29 04:09:41

202

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Kernel is a normal subgroup of the preimage

Published on 29 Mar 2026 - 4:09

score 169 · Answer 2 · 2016-09-20 02:40:48

169

Views

Prove $H=\lbrace x \in G: x^n =e \rbrace$ is a subgroup of group G.

Published on 20 Sep 2016 - 2:40

score 757 · Answer 3 · 2026-03-30 06:29:20

757

Views

Show that all the orbits have the cardinality $[N:N \cap \text{Stab } a]$ for some $a \in O_1$

Published on 30 Mar 2026 - 6:29

score 171 · Answer 4 · 2026-03-30 16:23:24

171

Views

Finding the Order of G, given subgroups

Published on 30 Mar 2026 - 16:23

score 1.7k · Answer 5 · 2026-03-26 01:34:38

1.7k

Views

$G$ is a $p$-group $\implies $ $G$ has a normal subgroup of $p^k \ \forall k$

Published on 26 Mar 2026 - 1:34

score 378 · Answer 6 · 2026-03-30 16:30:03

378

Views

Prove or disprove if G is an abelian and H is a normal subgroup of G,then H must be a cyclic

Published on 30 Mar 2026 - 16:30

score 221 · Answer 7 · 2026-03-26 08:02:23

221

Views

Suppose $N\unlhd G$ with $N\cong G/N\cong S$, $S$ a nonabelian finite simple group. Assume that $\operatorname{Out}(S)$ is solvable.

Published on 26 Mar 2026 - 8:02

score 51 · Answer 8 · 2016-09-29 19:02:52

51

Views

How could I prove this equation true?

Published on 29 Sep 2016 - 19:02

score 565 · Answer 9 · 2016-10-02 11:26:38

565

Views

Prove $H \lhd G$ and $G/H$ is abelian $\iff [G,G] \leq H$

Published on 02 Oct 2016 - 11:26

score 3.9k · Answer 10 · 2016-10-03 03:00:56

3.9k

Views

Size of orbit of $x$ divides the order of $G$

Published on 03 Oct 2016 - 3:00

score 243 · Answer 11 · 2016-10-04 14:44:01

243

Views

If a normal subgroup of $\mathbb{A}_n$ contains an element with cycle decomposition that has a cycle length $\geq4$, $N=\mathbb{A}_n$

Published on 04 Oct 2016 - 14:44

score 73 · Answer 12 · 2016-10-06 01:18:33

73

Views

What's the significance of using a generator to prove a cyclic subgroup?

Published on 06 Oct 2016 - 1:18

score 683 · Answer 13 · 2016-10-06 13:31:47

683

Views

Process behind proving a matrix subgroup is a cyclic subgroup?

Published on 06 Oct 2016 - 13:31

score 4.5k · Answer 14 · 2016-10-07 09:18:31

4.5k

Views

If every cyclic subgroup of a group G be normal in G, prove that every subgroup of G is normal in G.

Published on 07 Oct 2016 - 9:18

score 157 · Answer 15 · 2016-10-07 10:54:52

157

Views

Prove that $Q_8$ has a subgroup $H$ of order $2$ and $H$ is normal in $Q_8$

Published on 07 Oct 2016 - 10:54

List Question

Kernel is a normal subgroup of the preimage

Prove $H=\lbrace x \in G: x^n =e \rbrace$ is a subgroup of group G.

Show that all the orbits have the cardinality $[N:N \cap \text{Stab } a]$ for some $a \in O_1$

Finding the Order of G, given subgroups

$G$ is a $p$-group $\implies $ $G$ has a normal subgroup of $p^k \ \forall k$

Prove or disprove if G is an abelian and H is a normal subgroup of G,then H must be a cyclic

Suppose $N\unlhd G$ with $N\cong G/N\cong S$, $S$ a nonabelian finite simple group. Assume that $\operatorname{Out}(S)$ is solvable.

How could I prove this equation true?

Prove $H \lhd G$ and $G/H$ is abelian $\iff [G,G] \leq H$

Size of orbit of $x$ divides the order of $G$

If a normal subgroup of $\mathbb{A}_n$ contains an element with cycle decomposition that has a cycle length $\geq4$, $N=\mathbb{A}_n$

What's the significance of using a generator to prove a cyclic subgroup?

Process behind proving a matrix subgroup is a cyclic subgroup?

If every cyclic subgroup of a group G be normal in G, prove that every subgroup of G is normal in G.

Prove that $Q_8$ has a subgroup $H$ of order $2$ and $H$ is normal in $Q_8$

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