Question

Are these example subgroups?

score 41 · Answer 1 · 2015-04-20 18:26:37

41

Views

Are these example subgroups?

Published on 20 Apr 2015 - 18:26

score 745 · Answer 2 · 2015-04-21 23:11:34

745

Views

Do groups of prime order have one subgroup?

Published on 21 Apr 2015 - 23:11

score 95 · Answer 3 · 2026-03-27 04:16:53

95

Views

A question about direct product of subgroups.

Published on 27 Mar 2026 - 4:16

score 502 · Answer 4 · 2026-03-30 10:13:26

502

Views

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

Published on 30 Mar 2026 - 10:13

score 810 · Answer 5 · 2026-03-31 10:13:52

810

Views

Action of $G$ on the left cosets of $H$ giving a non-trivial homomorphism

Published on 31 Mar 2026 - 10:13

score 40 · Answer 6 · 2015-04-29 17:54:30

40

Views

Example of not normal subgroup $N$ such that not all orbits of $X$ under $N$ have the same length

Published on 29 Apr 2015 - 17:54

score 5.2k · Answer 7 · 2015-04-30 03:45:02

5.2k

Views

Show that $N(H)$ is the largest subgroup of $G$ in which $ H$ is normal.

Published on 30 Apr 2015 - 3:45

score 3.8k · Answer 8 · 2015-04-30 23:45:34

3.8k

Views

Show H is normal to G iff $N_G(H)=G$

Published on 30 Apr 2015 - 23:45

score 2.4k · Answer 9 · 2015-05-01 08:46:06

2.4k

Views

Is the intersection between a subgroup, and a normal subgroup, normal in the parent group?

Published on 01 May 2015 - 8:46

score 491 · Answer 10 · 2015-05-02 09:07:26

491

Views

If $G$ acts non-trivially on a set then it has a proper normal subgroup of finite index

Published on 02 May 2015 - 9:07

score 89 · Answer 11 · 2015-05-02 10:54:04

89

Views

No normal subgroup of a subgroup of $S_n$ imply the subgroup is the one of even permutations or consists of two elements

Published on 02 May 2015 - 10:54

score 106 · Answer 12 · 2015-05-03 02:46:18

106

Views

Normal subgroups and index problem

Published on 03 May 2015 - 2:46

score 82 · Answer 13 · 2026-03-31 10:14:44

82

Views

If $H\unlhd SL(2,\mathbb{Z})$ and $[SL(2,\mathbb{Z}):H]<\infty$ s.t. $H=\ker(\rho)$, then why is $|\operatorname{Im}(\rho)|<\infty$?

Published on 31 Mar 2026 - 10:14

score 74 · Answer 14 · 2015-05-06 02:54:27

74

Views

Please help me with proving a subgroup is normal

Published on 06 May 2015 - 2:54

score 508 · Answer 15 · 2026-03-30 02:11:36

508

Views

Group of order $135$ abelian and not cyclic

Published on 30 Mar 2026 - 2:11

List Question

Are these example subgroups?

Do groups of prime order have one subgroup?

A question about direct product of subgroups.

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

Action of $G$ on the left cosets of $H$ giving a non-trivial homomorphism

Example of not normal subgroup $N$ such that not all orbits of $X$ under $N$ have the same length

Show that $N(H)$ is the largest subgroup of $G$ in which $ H$ is normal.

Show H is normal to G iff $N_G(H)=G$

Is the intersection between a subgroup, and a normal subgroup, normal in the parent group?

If $G$ acts non-trivially on a set then it has a proper normal subgroup of finite index

No normal subgroup of a subgroup of $S_n$ imply the subgroup is the one of even permutations or consists of two elements

Normal subgroups and index problem

If $H\unlhd SL(2,\mathbb{Z})$ and $[SL(2,\mathbb{Z}):H]<\infty$ s.t. $H=\ker(\rho)$, then why is $|\operatorname{Im}(\rho)|<\infty$?

Please help me with proving a subgroup is normal

Group of order $135$ abelian and not cyclic

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