Timeline for Classification of automorphism groups of groups of order $p^4$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2014 at 18:43 | comment | added | Stefan Kohl♦ | The reason for the inefficiency of StructureDescription is mainly that originally there was the promise that the result should only depend on the isomorphism type of the group, and not on the way it is represented. Now as that promise in the GAP manual has been abandoned, it would be possible to speed up the function quite a lot -- of course at the 'cost' that the descriptions of some groups change. (I happen to be the author of a large part of StructureDescription.) | |
| Feb 10, 2014 at 15:33 | comment | added | Russ Woodroofe | Yes, StructureDescription is limited. But is there a better alternative for getting a human-readable description of groups, suitable for MathOverflow? (I guess one easy improvement would be to only ask for the structure of the outer automorphism group.) | |
| Feb 10, 2014 at 14:29 | comment | added | Max Horn | Ah, however, computing StructureDescription on each of the automorphism groups won't be instant. That's because of how StructureDescription works. But StructureDescription is not a very useful tool to begin with. Read its documentation for a lot of warnings about its limitations; it certainly isn't the right tool for a "classification" of a set of groups. | |
| Feb 10, 2014 at 14:27 | comment | added | Max Horn | I tried this in GAP 4.7.2 (actually, in a more recent developer version, but it shouldn't matter). With the autpgrp loaded in GAP (which, by the way, is normally loaded by default when you have it installed), computations are basically instant for e.g. 13^4, too. | |
| Feb 10, 2014 at 12:20 | comment | added | Derek Holt | Magma is returning the orders of the automorphism groups for reasonable sized primes almost instantly. But I think it is using the Eick/O'Brien package, so perhaps you need to tell GAP to use it. Example: [#AutomorphismGroup(SmallGroup(13^4,i)): i in [1..NumberOfSmallGroups(13^4)] ]; [ 26364, 748526688, 53466192, 4455516, 4112784, 342732, 53466192, 4455516, 685464, 685464, 116770163328, 116770163328, 695060496, 57578976, 610296923230525440 ] | |
| Feb 10, 2014 at 7:18 | comment | added | Giuliano Bianco | I'd add that thanks to prof. @russ-woodroofe reference to GAP I discovered that there is a specific package to compute automorphism groups of p-groups based on the p-group generation algorithm by Eamonn O'Brien. | |
| Feb 10, 2014 at 6:00 | history | answered | Russ Woodroofe | CC BY-SA 3.0 |