Question

Suppose $N\trianglelefteq G$ and $H\leqslant G$. If $\vert G/N \vert$ is prime prove $H\subseteq N$ or $ NH=G$

score 435 · Answer 1 · 2019-03-19 16:23:30

435

Views

Suppose $N\trianglelefteq G$ and $H\leqslant G$. If $\vert G/N \vert$ is prime prove $H\subseteq N$ or $ NH=G$

Published on 19 Mar 2019 - 16:23

score 79 · Answer 2 · 2019-03-20 08:00:26

79

Views

Show that $c(S) = \{a\in G : a\in gSg^{-1}\ \forall g\in G\}$ is normal in $G$

Published on 20 Mar 2019 - 8:00

score 35 · Answer 3 · 2026-03-25 09:24:10

35

Views

Internal Semidirect with Factors Isomorphic to "Outside" Groups

Published on 25 Mar 2026 - 9:24

score 266 · Answer 4 · 2019-03-21 17:00:59

266

Views

Nontrivial normal subgroup that doesn't contain commutator subgroup

Published on 21 Mar 2019 - 17:00

score 175 · Answer 5 · 2019-03-22 08:51:43

175

Views

How to show that $H$ is normal in $G$?

Published on 22 Mar 2019 - 8:51

score 68 · Answer 6 · 2019-03-23 09:23:33

68

Views

$C_G^n(g) \triangleleft C_G^{n + 1}$?

Published on 23 Mar 2019 - 9:23

score 142 · Answer 7 · 2026-03-19 15:23:49

142

Views

Group $N \triangleleft G$, $(|N|,|G/N|) = 1$, then $N$ is a characteristic subgroup of $G$.

Published on 19 Mar 2026 - 15:23

score 98 · Answer 8 · 2026-03-25 21:00:07

98

Views

Compact normal subgroups of connected groups

Published on 25 Mar 2026 - 21:00

score 88 · Answer 9 · 2019-03-27 16:37:08

88

Views

Is it always true that $g$ is bounded left-Engel element iff it belongs to an abelian subnormal subgroup?

Published on 27 Mar 2019 - 16:37

score 47 · Answer 10 · 2019-03-27 18:51:34

47

Views

Show that a Kernel of a natural mapping in normal groups is the intersection of these.

Published on 27 Mar 2019 - 18:51

score 58 · Answer 11 · 2019-03-29 13:07:12

58

Views

On non-trivial proper normal subgroups

Published on 29 Mar 2019 - 13:07

score 51 · Answer 12 · 2019-03-29 13:36:46

51

Views

A question about normal subgroups.

Published on 29 Mar 2019 - 13:36

score 1.3k · Answer 13 · 2026-03-26 19:39:37

1.3k

Views

If $H$ is not normal subgroup of $G$ then there are two left cosets of $H$ which multiplication is not a left coset of $H$

Published on 26 Mar 2026 - 19:39

score 772 · Answer 14 · 2026-03-26 21:34:59

772

Views

An application of the first (group) isomorphism theorem

Published on 26 Mar 2026 - 21:34

score 129 · Answer 15 · 2026-03-25 23:10:11

129

Views

Index of centralizer if $H\lhd G$ and $|H| < \infty$

Published on 25 Mar 2026 - 23:10

List Question

Suppose $N\trianglelefteq G$ and $H\leqslant G$. If $\vert G/N \vert$ is prime prove $H\subseteq N$ or $ NH=G$

Show that $c(S) = \{a\in G : a\in gSg^{-1}\ \forall g\in G\}$ is normal in $G$

Internal Semidirect with Factors Isomorphic to "Outside" Groups

Nontrivial normal subgroup that doesn't contain commutator subgroup

How to show that $H$ is normal in $G$?

$C_G^n(g) \triangleleft C_G^{n + 1}$?

Group $N \triangleleft G$, $(|N|,|G/N|) = 1$, then $N$ is a characteristic subgroup of $G$.

Compact normal subgroups of connected groups

Is it always true that $g$ is bounded left-Engel element iff it belongs to an abelian subnormal subgroup?

Show that a Kernel of a natural mapping in normal groups is the intersection of these.

On non-trivial proper normal subgroups

A question about normal subgroups.

If $H$ is not normal subgroup of $G$ then there are two left cosets of $H$ which multiplication is not a left coset of $H$

An application of the first (group) isomorphism theorem

Index of centralizer if $H\lhd G$ and $|H| < \infty$

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