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A066085
Orders of non-supersolvable groups.
5
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
OFFSET
1,1
COMMENTS
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, Dec 22 2003
LINKS
Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.
EXAMPLE
a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.
CROSSREFS
For primitive terms see A340517.
Sequence in context: A059691 A097060 A336657 * A340511 A094529 A270571
KEYWORD
nonn
AUTHOR
Reiner Martin, Dec 29 2001
EXTENSIONS
More terms from Des MacHale, Dec 22 2003
STATUS
approved