Timeline for Periodic Automorphism Towers
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2016 at 6:21 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 7, 2016 at 18:38 | comment | added | Justin Benfield | I further extended the list of $Aut$-stable groups up to order 511 (not doing order 512 anytime soon considering how many of them there are and how long it takes to test them). I already have made some interesting observations: They are all either centerless or have $Z(G)\simeq\mathbb{Z}_2$ (which are precisely the two groups that have trivial automorphism group, coincidence? I doubt it). | |
| Mar 7, 2016 at 18:34 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 7, 2016 at 16:26 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 6, 2016 at 14:23 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 2, 2016 at 7:28 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 2, 2016 at 1:54 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Mar 2, 2016 at 1:48 | comment | added | Justin Benfield | I figured out how to modify the for loop I was using to test these groups to allow me to tackle the order 256 is smaller pieces (to avoid prohibitive runtime), and managed to test all 56,092 groups of order 256, verifying my prediction that none are isomorphic to their own automorphism group. I continued the tests up to order 383 and found a few more groups, which I have added to my post. | |
| Dec 14, 2015 at 5:11 | history | edited | Justin Benfield | CC BY-SA 3.0 |
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| Dec 13, 2015 at 6:54 | comment | added | Justin Benfield | Update: I figured out how to get GAP to test all groups of order up to $n$ to see if they are stable or not, I have now have a complete list of stable groups of order up to 127 (took quite a bit of time for it test them all). The stable groups of order up to 127 have GAP ids: $(1,1)$, $(6,1)$, $(8,3)$, $(12,4)$, $(20,3)$, $(24,12)$, $(40,12)$, $(42,1)$, $(48,48)$, $(54,6)$, $(84,7)$, $(108,26)$, $(110,1)$, $(120,34)$, $(120,36)$. | |
| Dec 12, 2015 at 3:54 | review | Late answers | |||
| Dec 12, 2015 at 4:06 | |||||
| Dec 12, 2015 at 3:38 | history | answered | Justin Benfield | CC BY-SA 3.0 |