List questions from characteristic-subgroups

Published on 07 Oct 2011 - 3:14

265

Views

Quick way to determine characteristic subgroups

Published on 06 Aug 2020 - 17:33

307

Views

Fully invariant subgroups of the group $S_4$

Published on 07 Nov 2020 - 10:24

162

Views

Verbal Subgroups of $\mathbb{Z}^2$

Published on 14 Nov 2020 - 22:17

159

Views

Let $G$ be f.g. with $H\le G$ s.t. $[G:H]<\infty$. Then $\exists K\le H$ with $K\sqsubseteq G$ and $[G:K]<\infty$.

Published on 29 Dec 2020 - 18:25

49

Views

Lemma of Characterictic Subgroups

Published on 06 Apr 2021 - 15:32

43

Views

$\{0\}\times 3\mathbb{Z}/9\mathbb{Z}$ as a characteristic subgroup of $\mathbb{Z}/3\mathbb{Z} \times \mathbb{Z}/9\mathbb{Z}$

Published on 12 Jun 2021 - 16:30

134

Views

The characteristic subgroup of order $m$ (odd) in a group of order $2^nm$ with cyclic 2-sylow

Published on 20 Aug 2021 - 22:32

572

Views

Normal subgroup of a characteristic subgroup

Published on 16 Sep 2021 - 22:30

80

Views

If a subgroup is unique, is it characteristic?

Published on 24 Oct 2021 - 14:01

128

Views

If $G=\langle H,K\rangle$, then $G'=[H,K]$

Published on 27 Jun 2022 - 22:46

268

Views

If $H\trianglelefteq K$ and $K\text{ char } G$, then is $H\trianglelefteq G$?

Published on 30 Jun 2022 - 17:48

151

Views

Given $N$ char $G$, prove that $N\lt K \lt G$ and $K/N$ char $G/N$ implies $K$ char $G$

Published on 11 Oct 2022 - 15:34

52

Views

Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Published on 08 Dec 2022 - 16:10

247

Views

Isomorphism on a Sylow-$p$-subgroup of a group $G$.

Published on 25 Jan 2023 - 0:27

List Question

A simple question on characteristic subgroups

Quick way to determine characteristic subgroups

Fully invariant subgroups of the group $S_4$

Verbal Subgroups of $\mathbb{Z}^2$

Let $G$ be f.g. with $H\le G$ s.t. $[G:H]<\infty$. Then $\exists K\le H$ with $K\sqsubseteq G$ and $[G:K]<\infty$.

Lemma of Characterictic Subgroups

$\{0\}\times 3\mathbb{Z}/9\mathbb{Z}$ as a characteristic subgroup of $\mathbb{Z}/3\mathbb{Z} \times \mathbb{Z}/9\mathbb{Z}$

The characteristic subgroup of order $m$ (odd) in a group of order $2^nm$ with cyclic 2-sylow

Normal subgroup of a characteristic subgroup

If a subgroup is unique, is it characteristic?

If $G=\langle H,K\rangle$, then $G'=[H,K]$

If $H\trianglelefteq K$ and $K\text{ char } G$, then is $H\trianglelefteq G$?

Given $N$ char $G$, prove that $N\lt K \lt G$ and $K/N$ char $G/N$ implies $K$ char $G$

Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Isomorphism on a Sylow-$p$-subgroup of a group $G$.

Trending Questions

Popular # Hahtags

Popular Questions