Timeline for Sylow 2-subgroups of finite groups in which every subgroup of order 4 is cyclic
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| S Oct 13, 2020 at 8:29 | history | suggested | gmvh |
Added top-level and "reference-request" tags
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| Oct 13, 2020 at 7:50 | review | Suggested edits | |||
| S Oct 13, 2020 at 8:29 | |||||
| Oct 13, 2020 at 5:40 | comment | added | quaternion | Thank you @GeoffRobinson! Indeed the proof was very easy. | |
| Oct 12, 2020 at 22:02 | review | Close votes | |||
| Oct 18, 2020 at 9:08 | |||||
| Oct 12, 2020 at 20:04 | comment | added | Geoff Robinson | Let $S$ be a Sylow $2$-subgroup of $G$. Then $Z(S)$ contains an element $t$ of order $2$. Furthermore, $t$ is the only involution (element of order two) of $S$, for if there were another involution $u \in S$, then $\langle t,u \rangle$ is a non-cyclic subgroup of $S$ of order $4$. It is indeed true that a $2$-group which contains a unique involution is either cyclic or generalized quaternion. This proved in many group theory texts, for example Finite Groups by D. Gorenstein. | |
| Oct 12, 2020 at 18:55 | review | First posts | |||
| Oct 12, 2020 at 19:57 | |||||
| Oct 12, 2020 at 18:52 | history | asked | quaternion | CC BY-SA 4.0 |