Timeline for Automorphisms of non-abelian groups of order $ p^3$
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2016 at 13:37 | review | Close votes | |||
| Jul 18, 2016 at 19:23 | |||||
| S Jul 18, 2016 at 12:19 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
corrected mathematical notations
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| S Jul 18, 2016 at 12:19 | history | suggested | Styles | CC BY-SA 3.0 |
corrected mathematical notations
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| Jul 18, 2016 at 12:18 | review | Suggested edits | |||
| S Jul 18, 2016 at 12:19 | |||||
| Aug 22, 2014 at 14:02 | history | edited | Lee Mosher |
edited tags
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| Aug 22, 2014 at 9:45 | review | Close votes | |||
| Aug 22, 2014 at 19:02 | |||||
| Jul 30, 2014 at 22:54 | answer | added | Giuliano Bianco | timeline score: 6 | |
| Apr 30, 2014 at 16:37 | comment | added | Geoff Robinson | Note that when $p = 2,$ the groups you describe coincide ( they are both dihedral of order $8$). There are still two isomorphis types of non-Abelian groups of order $8,$ but the quaternion group of order $8$ needs to be included in that case. | |
| Apr 3, 2013 at 7:21 | vote | accept | Soluble | ||
| Nov 7, 2012 at 1:03 | answer | added | Thomas | timeline score: 6 | |
| Feb 23, 2011 at 9:11 | comment | added | Steve D | @Rahul: I deleted my answer (I think), and instead typed everything up into a PDF. You can email me and I'd be glad to send it to you. | |
| Feb 23, 2011 at 3:55 | comment | added | Soluble | This example I couldn't see in any Graduate Studies book; it is not also given as an exercise. Late, I found that it is an exercise in the book "Structure of Groups of Prime Power Order". When working such examples in GAP, it gives the order of Automorphism group of these groups quickly, but it is not giving information about structure. | |
| Feb 22, 2011 at 15:32 | comment | added | Jim Humphreys | It's instructive to work out such examples from scratch, but it's also important to realize that this has certainly been done before and is most likely written down in detail (somewhere). With over a century of literature on group theory including many books, it could take a while to locate such information; maybe it's quicker to do it yourself. Anyway, it's also useful to organize the possible methods such as generators and relations, linear representations, geometric realizations. GAP has its limitations for giving insight. | |
| Feb 22, 2011 at 8:29 | answer | added | Tom De Medts | timeline score: 11 | |
| Jan 21, 2011 at 6:02 | comment | added | Soluble | In GAP, I tried for first group with p=3,( i.e. G=Z/3Z x Z/3Z): Z/3Z); but no output. It gives |Aut(G)|=432, but no structure description. So I am looking theoretically. I did following: since any automorphism of G fixes center(not necessarily pointwise), there is natural homomorphism f:Aut(G) --> Aut(G/Z(G)), where |Z(G)|=p, and G/Z(G)=Z/pZ x Z/pZ, Aut(G/Z(G))=GL(2,p). We can show that f is surjective with kernel Z/pZ x Z/pZ. Hence |Aut(G)|=(p^2).|GL(2,p)|=(p^3).(p+1).(p-1)^2. I couldn't proceed further. | |
| Jan 21, 2011 at 5:42 | answer | added | Chris Gerig | timeline score: 8 | |
| Jan 21, 2011 at 5:11 | comment | added | Mariano Suárez-Álvarez | Have you tried asking GAP? | |
| Jan 21, 2011 at 5:01 | history | asked | Soluble | CC BY-SA 2.5 |