Timeline for Extending an infinite simple group
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2015 at 11:37 | history | edited | 喻 良 | CC BY-SA 3.0 |
added 223 characters in body
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| Oct 30, 2015 at 11:17 | vote | accept | 喻 良 | ||
| Oct 30, 2015 at 10:59 | answer | added | Derek Holt | timeline score: 11 | |
| Oct 30, 2015 at 10:44 | comment | added | 喻 良 | If this argument works, then by a Skolemization including $H$, it holds for any cardinal $\kappa\geq|H|$. | |
| Oct 30, 2015 at 10:33 | comment | added | Derek Holt | In general, if $|H| = \kappa$ with $\kappa$ infinite, then you can embed $H$ in ${\rm Sym}(H)$ by Cayley's Theorem, and this induces an embedding of $H$ into the simple group ${\rm Sym}(H)/K$, where $K$ consists of those permutation with support less than $\kappa$, which has cardinalty $2^\kappa$. So, the answer is yes if you assume GCH. Without that, it could be difficult. | |
| Oct 30, 2015 at 10:10 | comment | added | Derek Holt | Every finite group is a subgroup of $A_n$ for all sufficiently large $n$ so it is certainly true that every finite simple group embeds properly in a larger one. | |
| Oct 30, 2015 at 9:09 | history | edited | Myshkin | CC BY-SA 3.0 |
minor latex edit
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| Oct 30, 2015 at 8:58 | history | asked | 喻 良 | CC BY-SA 3.0 |