Question

$H$ and $K$ are normal subgroups of a group $G$ with $K \le H$, then $aK =H \iff a \in H$

score 421 · Answer 1 · 2020-07-26 08:34:27

421

Views

$H$ and $K$ are normal subgroups of a group $G$ with $K \le H$, then $aK =H \iff a \in H$

Published on 26 Jul 2020 - 8:34

score 138 · Answer 2 · 2026-03-26 19:23:43

138

Views

Confusion about factor groups

Published on 26 Mar 2026 - 19:23

score 181 · Answer 3 · 2020-07-28 09:13:22

181

Views

$N\subseteq G_x$ then is $N$ in the kernel of the group action

Published on 28 Jul 2020 - 9:13

score 946 · Answer 4 · 2026-03-28 11:13:34

946

Views

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

Published on 28 Mar 2026 - 11:13

score 373 · Answer 5 · 2016-07-09 02:32:15

373

Views

If $G/N\cong H$ then $G=NH$?

Published on 09 Jul 2016 - 2:32

score 557 · Answer 6 · 2016-07-11 06:18:47

557

Views

finding total no. of subgroups of a group

Published on 11 Jul 2016 - 6:18

score 1.2k · Answer 7 · 2016-07-12 05:43:46

1.2k

Views

Find the Quotient group of normal subgroup of order 4 of quaternion group.

Published on 12 Jul 2016 - 5:43

score 514 · Answer 8 · 2026-03-26 16:10:08

514

Views

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

Published on 26 Mar 2026 - 16:10

score 86 · Answer 9 · 2016-07-16 08:46:24

86

Views

Normal subgroup.

Published on 16 Jul 2016 - 8:46

score 143 · Answer 10 · 2016-07-29 18:51:07

143

Views

Proving $core_G(H)$ is non-trivial.

Published on 29 Jul 2016 - 18:51

score 1k · Answer 11 · 2016-08-06 18:43:16

1k

Views

Let $G$ be a non-abelian group, $|G|=6$. Then there exists $a\in G$ such that $o(a)=2$. Is it true that $\langle a\rangle$ is not normal in $G$?

Published on 06 Aug 2016 - 18:43

score 223 · Answer 12 · 2016-08-07 14:30:24

223

Views

one lemma for proving Butterfly lemma

Published on 07 Aug 2016 - 14:30

score 2.9k · Answer 13 · 2026-03-26 06:21:44

2.9k

Views

Every normal subgroup of a solvable group must have an abelian subgroup which is normal in G.

Published on 26 Mar 2026 - 6:21

score 33 · Answer 14 · 2016-08-21 00:02:06

33

Views

Counter example to "$(P_1...P_{r-1})\cap P_r = \{ e \}$ if $P_i \cap P_j = \{ e \}$ and $P_i$ is normal in $G$"

Published on 21 Aug 2016 - 0:02

score 172 · Answer 15 · 2026-03-28 12:58:17

172

Views

How do you prove $(P_1...P_{r-1}) \cap P_r = \{ e \}$ for normal Sylow subgroups $P_i$?

Published on 28 Mar 2026 - 12:58

List Question

$H$ and $K$ are normal subgroups of a group $G$ with $K \le H$, then $aK =H \iff a \in H$

Confusion about factor groups

$N\subseteq G_x$ then is $N$ in the kernel of the group action

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

If $G/N\cong H$ then $G=NH$?

finding total no. of subgroups of a group

Find the Quotient group of normal subgroup of order 4 of quaternion group.

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

Normal subgroup.

Proving $core_G(H)$ is non-trivial.

Let $G$ be a non-abelian group, $|G|=6$. Then there exists $a\in G$ such that $o(a)=2$. Is it true that $\langle a\rangle$ is not normal in $G$?

one lemma for proving Butterfly lemma

Every normal subgroup of a solvable group must have an abelian subgroup which is normal in G.

Counter example to "$(P_1...P_{r-1})\cap P_r = \{ e \}$ if $P_i \cap P_j = \{ e \}$ and $P_i$ is normal in $G$"

How do you prove $(P_1...P_{r-1}) \cap P_r = \{ e \}$ for normal Sylow subgroups $P_i$?

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