Timeline for Groups all of whose extensions are split
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2022 at 7:24 | history | edited | YCor | CC BY-SA 4.0 |
moved correction notice to the end since now inessential
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| Oct 30, 2021 at 17:10 | comment | added | Brauer Suzuki | This is a theorem of [J. S. Rose, Splitting properties of group extensions, Proc. London Math. Soc. (3) 22 (1971), 1–23]. | |
| Oct 8, 2021 at 8:12 | comment | added | YCor | @MarianoSuárez-Álvarez This is correct and there were explicit instances of my previous construction which provided a split extension, contrary to my claim. I have therefore rewritten the proof, being more careful in the embedding into a group $S$. | |
| Oct 8, 2021 at 8:11 | history | undeleted | YCor | ||
| Oct 8, 2021 at 8:10 | history | edited | YCor | CC BY-SA 4.0 |
rewrote proof
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| Oct 8, 2021 at 8:03 | history | edited | YCor | CC BY-SA 4.0 |
rewrote proof
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| Oct 8, 2021 at 7:22 | history | edited | YCor | CC BY-SA 4.0 |
explained mistake
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| Oct 8, 2021 at 7:07 | history | deleted | YCor | via Vote | |
| Oct 8, 2021 at 5:59 | comment | added | Mariano Suárez-Álvarez | I sat down to write this out in detail. In the second paragraph, certainly the centralizer of $G$ in $G\rtimes L$ contains $Z\rtimes C_L(G)$, but why is it equal to it? An element $(g,l)$ in $G\rtimes L$ such that $l$ acts on $G$ as the inner automorphism $g^{-1}(?)g$ is also in the cetralizer :-1 | |
| Oct 7, 2021 at 22:05 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo
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| Oct 7, 2021 at 21:53 | history | edited | LSpice | CC BY-SA 4.0 |
Missing space
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| Oct 7, 2021 at 21:53 | comment | added | LSpice | When you say "the semidirect product $A^2 \rtimes \langle u\rangle$ contains $Z \times \{0\}$", should it be ""contains $A \times \{0\}$" (presumably embedded as $A \times \{0\} \subseteq A^2 \to A^2 \rtimes \langle u\rangle$)? | |
| Oct 7, 2021 at 20:02 | comment | added | Mariano Suárez-Álvarez | I've been googling for a while, actually! :-) The edit is just what I was looking for, thanks. | |
| Oct 7, 2021 at 20:01 | comment | added | YCor | @MarianoSuárez-Álvarez This probably appears somewhere in MO and in the literature, I could prove it (using choice) but I gave an easy choice-free proof of a weaker statement which is enough. | |
| Oct 7, 2021 at 20:00 | history | edited | YCor | CC BY-SA 4.0 |
added proof of embedding
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| Oct 7, 2021 at 19:12 | comment | added | Mariano Suárez-Álvarez | Thanks! Do you have a reference for the embedding of the Z into the center of a perfect group? | |
| Oct 7, 2021 at 9:52 | history | answered | YCor | CC BY-SA 4.0 |