Timeline for $2$-power-torsion elements of a group
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2019 at 12:54 | comment | added | Geoff Robinson | Just to build on Derek Holt's example, there are many simple examples. For example, let $G$ be any of the simple groups ${\rm SL}(2,2^{n})$ where $n >1.$ Then $G$ has a unique conjugacy class of involutions, so f $P$ is a Sylow $2$-subgroup of $G$ and $T$ is a (proper) subgroup of $P$ of order $2,$ we have $\bigcup_{g \in G} g^{-1}Tg = \bigcup_{g \in G} g^{-1}Pg.$ | |
| Jan 7, 2019 at 1:26 | comment | added | user90517 | @Derek Right, thank you! | |
| Jan 6, 2019 at 21:10 | review | Close votes | |||
| Feb 2, 2019 at 3:05 | |||||
| Jan 6, 2019 at 20:54 | comment | added | Derek Holt | What about $G=A_4$ and $H$ a subgroup of order $2$. Then $P \lhd G$ and $\cup_{g \in G} g^{-1}Hg = P$. | |
| Jan 6, 2019 at 19:55 | review | First posts | |||
| Jan 6, 2019 at 21:40 | |||||
| Jan 6, 2019 at 19:53 | history | asked | user90517 | CC BY-SA 4.0 |