Timeline for Does O'Nan-Scott depend on CFSG?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 15, 2014 at 17:21 | vote | accept | Nick Gill | ||
| Jan 30, 2014 at 9:15 | comment | added | Michael Giudici | Yes the LPS paper in in JAustMS and only proves the `strong' version. I have just checked Scott's paper and he does indeed prove the weak version. | |
| Jan 29, 2014 at 14:11 | comment | added | Nick Gill | Michael, I do have the LPS-paper (in J. Aust. MS, right?)... I think it proves the `strong' version only... But I'll have to check. | |
| Jan 28, 2014 at 9:10 | comment | added | Michael Giudici | From memory there is a full proof of what you are calling the weak version in the paper by Scott, but I don't have it to hand at the moment. | |
| Jan 28, 2014 at 9:06 | comment | added | Michael Giudici | It is rarely the case in applications that you need the structure of twisted wreath product groups. Usually it is just enough to know that there is a nonabelian regular minimal normal subgroup which is unique. Have you looked at the paper by Liebeck, Praeger and Saxl? | |
| Jan 24, 2014 at 9:55 | history | edited | Derek Holt | CC BY-SA 3.0 |
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| Jan 23, 2014 at 17:35 | comment | added | Jim Humphreys | @Derek: I've inserted the LaTeX command for the wreath symbol, which is just \wr | |
| Jan 23, 2014 at 17:33 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jan 23, 2014 at 15:50 | comment | added | Derek Holt | The account in Cameron's book is more concise, but he refers to Dixon and Mortimer for more details. The Schreier Conjecture is used in the proof of Thm 4.7 B (ii) of D&M, and without that you could have groups with a nonabelian regular normal subgroup $N$ in which the point stabilizer had a nonabelian simple subgroup that fixed, and induced outer automorphisms of, all of the simple direct factors of $N$. So you would need to rule that out somehow. | |
| Jan 23, 2014 at 14:57 | comment | added | Nick Gill | Hi Derek, thanks for your answer. Your summary is exactly in line with how I understand the situation.... It'd be great if someone could give a reference for a full proof of the weak version that didn't use Schreier. (It should be extractable from Dixon & Mortimer, but I haven't the wherewithal to do that just now.) I'm also intrigued as to how seriously people have tried to prove the strong version without using Schreier? If one didn't use Schreier, I wonder what could be said? | |
| Jan 23, 2014 at 14:21 | history | answered | Derek Holt | CC BY-SA 3.0 |