cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A066085 Orders of non-supersolvable groups.

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%I A066085 #14 Oct 30 2022 18:19:59
%S A066085 12,24,36,48,56,60,72,75,80,84,96,108,112,120,132,144,150,156,160,168,
%T A066085 180,192,196,200,204,216,224,225,228,240,252,264,276,280,288,294,300,
%U A066085 312,320,324,336,348,351,360,363,372,375,384,392,396,400,405,408,420
%N A066085 Orders of non-supersolvable groups.
%C A066085 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.
%C A066085 All multiples of non-supersolvable orders are non-supersolvable orders. - _Des MacHale_, Dec 22 2003
%H A066085 B. Huppert, <a href="https://eudml.org/doc/169349">Über das Produkt von paarweise vertauschbaren zyklischen Gruppen</a>, Math. Z. 58 (1954).
%H A066085 Des MacHale and J. Manning, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Manning/manning5.html">Converse Lagrange Theorem Orders and Supersolvable Orders</a>, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.
%e A066085 a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.
%Y A066085 Cf. A000001, A066083, A340511.
%Y A066085 For primitive terms see A340517.
%K A066085 nonn
%O A066085 1,1
%A A066085 _Reiner Martin_, Dec 29 2001
%E A066085 More terms from _Des MacHale_, Dec 22 2003