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A060793
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Orders of finite perfect groups (groups such that G = G' where G' is the commutator subgroup of G).
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10
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1, 60, 120, 168, 336, 360, 504, 660, 720, 960, 1080, 1092, 1320, 1344, 1920, 2160, 2184, 2448, 2520, 2688, 3000, 3420, 3600, 3840, 4080, 4860, 4896, 5040, 5376, 5616, 5760, 6048, 6072, 6840, 7200, 7500, 7560, 7680, 7800, 7920, 9720, 9828, 10080, 10752
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This comment is about the four sequences A001034, A060793, A056866, A056868: The Feit Thompson theorem says that a finite group with odd order is solvable, hence apart from the first trivial term of A060793 all the other numbers in these sequences are even.
Since a non-cyclic simple group is perfect this sequence contains A001034 and since a perfect group is non-solvable this sequence is a subsequence of A056866 (apart from the initial term).
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REFERENCES
| D. Holt and W. Plesken, Perfect Groups, Oxford University Press, 1989.
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LINKS
| T. Leinster, Perfect numbers and groups
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EXAMPLE
| A_{5} is perfect since it is equivalent to A_{5}'.
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CROSSREFS
| Cf. A001034, A056866.
Sequence in context: A096490 A056866 A098136 * A169823 A087004 A177871
Adjacent sequences: A060790 A060791 A060792 * A060794 A060795 A060796
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KEYWORD
| nonn
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 26 2001
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