Timeline for Names of finite groups
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2016 at 18:32 | history | edited | Tim Dokchitser | CC BY-SA 3.0 |
added 188 characters in body
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| Apr 24, 2011 at 12:47 | answer | added | JMcKay | timeline score: 6 | |
| Dec 8, 2010 at 0:17 | answer | added | M.Z. | timeline score: 4 | |
| Dec 7, 2010 at 18:35 | comment | added | S. Carnahan♦ | Noah Snyder has suggested the notation $D_{2 \cdot n}$, as an unambiguous compromise for dihedral groups. | |
| Dec 7, 2010 at 15:37 | history | edited | Tim Dokchitser | CC BY-SA 2.5 |
minor corrections
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| Dec 7, 2010 at 15:35 | comment | added | Tim Dokchitser | @Nick, Jack & Theo: Thank you, that's helpful! | |
| Dec 6, 2010 at 19:43 | comment | added | ndkrempel | Have you looked into what the GAP function StructureDescription currently does? Details can be found in the manual: gap-system.org/Manuals/doc/htm/ref/CHAP037.htm#SECT006 | |
| Dec 6, 2010 at 16:23 | comment | added | Theo Johnson-Freyd | Unfortunately, we all still publish paper in Dead Tree. If you use a more modern graphical user interface, namely Light Emitting Diode, then you can usually provide greater functionality to your readers: allow them to click or double click or right click or whatever on each name for more information on it. (Such hyperlinking is also available in Dead Tree, of course, in the form of footnotes, endnotes, appendices, and references.) | |
| Dec 6, 2010 at 15:15 | comment | added | Jack Schmidt | @Tim: If you are interested, email me about some of the pitfalls of such a function. We've had several years of experience with providing such a function to users, and have discovered some non-obvious issues (that are a hassle to type in this interface). | |
| Dec 6, 2010 at 14:59 | comment | added | Jack Schmidt | In particular, for order 32 there are three groups with modular subgroup lattices but in which normality is not transitive; one of these is an o-m-c, but the other two are not. The name is only used for order 16, and I think only because it gives a name to one of the groups without an otherwise descriptive name. | |
| Dec 6, 2010 at 14:54 | comment | added | Jack Schmidt | I just made up "other-maximal-cyclic" since it had no given name in Gorenstein or Huppert. When it has order 16, it is also called the modular group (it being rare amongst groups of order 16 to have a modular subgroup lattice), but the article is about the infinite family. | |
| Dec 6, 2010 at 14:12 | comment | added | j.p. | About your example to canonical conventions: $(C_5 \rtimes C_4)\times C_5$ leaves only two options (assuming it's not a direct product): faithful action of $C_4$ or not. As $(C_5 \times C_5)\rtimes C_4$ allows also the action of $C_4$ to be fixed point free, new possibilities arise, and it is more ambiguous, and hence worse. | |
| Dec 6, 2010 at 13:50 | comment | added | Tim Dokchitser | @KConrad: I suppose I'll have an option IAmAGroupTheorist:boolean in my code to deal with dihedral groups then. @Jonathan: My OMC16 comes from the last paragraph of en.wikipedia.org/wiki/Quasidihedral_group, I don't know if that's the same as a modular group. What is the modular group of order 16 (as generators and relations or whatever)? | |
| Dec 6, 2010 at 13:47 | answer | added | Ken W. Smith | timeline score: 6 | |
| Dec 6, 2010 at 13:34 | comment | added | KConrad | Jonathan, I thought the notation for the dihedral groups is standard: group theorists write the dihedral group of order 2n as D_{2n} and everyone else (?) writes the group as D_n. | |
| Dec 6, 2010 at 12:49 | comment | added | Jonathan Kiehlmann | I've not heard of that notation, but I am not that much of a finite group theorist (I've never had to use the ATLAS, for one thing). I assumed that was what you meant by $C_5\rtimes C_4$, but that makes sense. Is $OMC_{16}$ what some people would call the modular group of order $16$? I think notation in this area is highly non-standardised: even the notation of the dihedral groups are not standard! | |
| Dec 6, 2010 at 12:48 | comment | added | Someone | $G_{20}$? I'd call it $F_{20}$ as it is the Frobenius group of order $20$. So good luck with finding names! | |
| Dec 6, 2010 at 12:41 | comment | added | Tim Dokchitser | $C_5\rtimes C_4$ with faithful action, I know that some people call it $G_{20}$ but I don't know to which extent this is a standard notation | |
| Dec 6, 2010 at 12:33 | comment | added | Jonathan Kiehlmann | What is $G_{20}$? | |
| Dec 6, 2010 at 12:08 | history | asked | Tim Dokchitser | CC BY-SA 2.5 |