List questions from derived-subgroup | MathQA

Show that the twisted commutator, $T_g = \{x \in G \mid \exists k\in\Bbb Z, xgx^{-1} = g^k\}\le G$ for some $g \in G$ of finite order

Published on 01 Jun 2022 - 2:43

A problem in group theory and representation theory.

Published on 25 Jun 2022 - 4:27

Quick question about metabelian group

Published on 11 Jul 2022 - 20:56

$\{ a \mid a\not \in [G,G],\ a \in Z(G) \} \cup \{e\}$ is a group or not

Published on 13 Jul 2022 - 12:05

Request vetting of understanding of problem on commutator subgroups.

Published on 13 Jul 2022 - 12:29

Commutator subgroup of connected group.

Published on 08 Aug 2022 - 16:53

Let $H = \langle X \rangle$ then $H' = \langle [x_1, x_2]^h \mid x_1, x_2 \in X, h \in H \rangle$

Published on 17 Dec 2022 - 15:38

In $G/K(G)$ for commutator group $K(G)$, it is said that $[a][b]=[a][b][b^{-1}a^{-1}ba]=[a][b][b^{-1}][a][b][a]=[b][a].$ Why the first equality?

Published on 21 Jan 2023 - 16:44

If $F$ is free and $R$ is normal in $F$, then $F/R'$ is torsion-free, where $R'=[R,R]$

Published on 21 Jan 2023 - 21:22