Timeline for Intersections of products of Sylow $p$-subgroups
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2018 at 13:39 | comment | added | Glasby | @Nick the paper Alavi, Seyed Hassan; Burness, Timothy C. Large subgroups of simple groups. J. Algebra 421 (2015), 187–233 characterizes pairs $(G,H)$ with $G$ simple and $|H|\geqslant |G|^{1/3}$. | |
| Feb 9, 2018 at 13:01 | history | edited | Padraig Ó Catháin | CC BY-SA 3.0 |
Clarified the questions, should be for all $p$, not fixed $p$.
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| Feb 9, 2018 at 6:13 | answer | added | Glasby | timeline score: 4 | |
| Dec 22, 2017 at 12:37 | comment | added | Padraig Ó Catháin | Thanks Nick - this is helpful! I just saw a paper on the arxiv which deals with cross characteristic cases: arxiv.org/pdf/1712.05899.pdf | |
| Dec 19, 2017 at 12:14 | comment | added | Nick Gill | I seem to recall that there is a theorem that characterizes the simple groups $G$ which have a Sylow $p$-subgroup with order at least $\sqrt[3]{|G|}$. (This article comes close -- iopscience.iop.org/article/10.1070/SM1982v043n03ABEH002453 -- but I can't access it to check it gives the full details.) Anyway, I believe that the only such FSG's are $PSL_2(q)$ and $Suz(q)$ -- presumably this could be checked reasonably easily using CFSG. My feeling is that this could be used to show that any family of groups $G$ which (asymptotically) satisfies $|G|<p^{3-\varepsilon}$ must be solvable. | |
| Dec 18, 2017 at 22:45 | history | edited | Padraig Ó Catháin | CC BY-SA 3.0 |
As suggested by Luc Guyot
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| Dec 18, 2017 at 18:09 | history | asked | Padraig Ó Catháin | CC BY-SA 3.0 |