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Search: id:A066085
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| A066085 |
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Orders of non-supersolvable groups. |
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+0
2
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| 12, 24, 36, 48, 56, 60, 72, 75, 80, 84, 96, 108, 112, 120, 132, 144, 150, 156, 160, 168, 180, 192, 196, 200, 204, 216, 224, 225, 228, 240, 252, 264, 276, 280, 288, 294, 300, 312, 320, 324, 336, 348, 351, 360, 363, 372, 375, 384, 392, 396, 400, 405, 408, 420
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.
All multiples of non-supersolvable orders are non-supersolvable orders. - Des MacHale (d.machale(AT)ucc.ie), Dec 22 2003
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REFERENCES
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B. Huppert, Ueber das Produkt von paarweise vertauschbaren zyklischen Gruppen, Math. Z. 58 (1954).
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EXAMPLE
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a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.
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CROSSREFS
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Cf. A000001, A066083.
Sequence in context: A103292 A059691 A097060 this_sequence A094529 A044852 A121578
Adjacent sequences: A066082 A066083 A066084 this_sequence A066086 A066087 A066088
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KEYWORD
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nonn
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AUTHOR
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Reiner Martin (reinermartin(AT)hotmail.com), Dec 29 2001
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EXTENSIONS
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More terms from Des MacHale (d.machale(AT)ucc.ie), Dec 22 2003
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