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.

A198342 Number of non-solvable transitive permutation groups for polynomials of degree n.

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%I A198342 #27 Sep 08 2022 08:45:59
%S A198342 0,0,0,0,2,4,3,5,4,21,4,36,3,27,40,49,5,91,2,358,56,27,3,807,79,26,64,
%T A198342 617,2,1896,4
%N A198342 Number of non-solvable transitive permutation groups for polynomials of degree n.
%C A198342 For prime degrees of polynomials see A201443.
%C A198342 All non-solvable groups are non-commutative.
%C A198342 Is this the same as A124938 ? - _R. J. Mathar_, Oct 04 2018
%H A198342 A. Bialostocki and T. Shaska, <a href="http://arxiv.org/abs/math/0601397">Galois groups of prime degree polynomials with nonreal roots</a>, 2006.
%e A198342 a(4)=0 because for quartic polynomials all groups are solvable.
%e A198342 a(5)=2 because for quintic polynomials we have two non-solvable groups: A(5) and S(5).
%o A198342 (Magma) // for a(16):
%o A198342 for g in [1..1954] do
%o A198342 G:=TransitiveGroup(16,g);
%o A198342 IsSolvable(G);
%o A198342 end for
%Y A198342 Cf. A002106, A131932.
%K A198342 nonn,hard,more
%O A198342 1,5
%A A198342 _Artur Jasinski_, Oct 23 2011