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A059773
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Maximum size of Aut(G) where G is a finite group of order n.
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2
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1, 1, 2, 6, 4, 6, 6, 168, 48, 20, 10, 24, 12, 42, 8, 20160, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| If n = 2^k then take G to be (Z/2Z)^k, the Abelian group with n=2^k elements and characteristic two. It is generated by any k linearly independent (non-identity) elements, so the automorphism group has size (n-1)(n-2)(n-4)...(n-2^(k-1)), which grows as n^log n. I think one can show that this is optimal for n=2^k and furthermore that this has the highest rate of growth for any infinite sequence of n's - Michael Kleber, Feb 21, 2001.
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EXAMPLE
| The corresponding groups are 1, Z2, Z3, (Z2)^2, Z5, S3, Z7, (Z2)^3, (Z3)^2, D5, Z11, A4, Z13, D7, Z15, (Z2)^4, Z17, ...
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CROSSREFS
| Sequence in context: A065630 A110633 A119250 * A127399 A151689 A202347
Adjacent sequences: A059770 A059771 A059772 * A059774 A059775 A059776
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KEYWORD
| nonn,nice,more
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AUTHOR
| Victor S. Miller (victor(AT)idaccr.org), Feb 21 2001
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EXTENSIONS
| More terms from Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 09 2001
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