Timeline for 5/8 bound in group theory
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2017 at 21:41 | comment | added | Alexander Chervov | Seems link to pdf is broken now | |
| Jul 18, 2017 at 19:15 | comment | added | Alexander Chervov | Just for record: generalization to three or more commuting elements is asked later: mathoverflow.net/questions/107904/… (Stragely it is not appear in "Linked" ) | |
| Jun 29, 2016 at 6:28 | comment | added | yakov | See also Chapter 11 in Berkovich-Zhmud', Characters of Finite Groups, Part 1. | |
| Mar 20, 2012 at 17:48 | vote | accept | john mangual | ||
| Mar 20, 2012 at 15:28 | history | edited | john mangual | CC BY-SA 3.0 |
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| Mar 20, 2012 at 13:42 | answer | added | Geoff Robinson | timeline score: 21 | |
| Mar 20, 2012 at 7:27 | comment | added | Geoff Robinson | Robert Guralnick and I have a Journal of Algebra Article called "On the Commuting Probability in Finite Groups" (~2006) where we discuss at some length links between the commuting probability and character theory among other things. Much of the paper is reasonably elementary, including a proof that that the commuting probabilty tends to $0$ as $[G:F(G) \to \infty,$ where $F(G)$ is the largest nilpotent nomal subgroup of the finite group $G.$ I am not sure whether this paper would help for other algebraic systems though. | |
| Mar 20, 2012 at 6:01 | answer | added | Igor Pak | timeline score: 48 | |
| Mar 20, 2012 at 5:21 | comment | added | Steve D | Any group with center of index 4 realizes this bound. (This is an iff). | |
| Mar 20, 2012 at 5:03 | comment | added | john mangual | Yeah, I dug up the article by Gustafson. This question appears as an exercise. Both groups you mention have order 8. | |
| Mar 20, 2012 at 5:00 | comment | added | Gerhard Paseman | A nice version would be to ask this for finite loops or quasigroups. Gerhard "Ask Me About System Design" Paseman, 2012.03.19 | |
| Mar 20, 2012 at 4:48 | history | edited | john mangual | CC BY-SA 3.0 |
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| Mar 20, 2012 at 4:42 | answer | added | Will Sawin | timeline score: 130 | |
| Mar 20, 2012 at 4:40 | comment | added | Will Sawin | That formula can't be quite right, since the term on the left is $<1$ and the term on the right is $>1$. Presumably you're off by a factor of $|G|$? The quaternions and $D4$ realize that bound. | |
| Mar 20, 2012 at 4:35 | history | asked | john mangual | CC BY-SA 3.0 |