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Number of non-solvable transitive permutation groups for polynomials of degree n.
1

%I #27 Sep 08 2022 08:45:59

%S 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 617,2,1896,4

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

%C For prime degrees of polynomials see A201443.

%C All non-solvable groups are non-commutative.

%C Is this the same as A124938 ? - _R. J. Mathar_, Oct 04 2018

%H 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 a(4)=0 because for quartic polynomials all groups are solvable.

%e a(5)=2 because for quintic polynomials we have two non-solvable groups: A(5) and S(5).

%o (Magma) // for a(16):

%o for g in [1..1954] do

%o G:=TransitiveGroup(16,g);

%o IsSolvable(G);

%o end for

%Y Cf. A002106, A131932.

%K nonn,hard,more

%O 1,5

%A _Artur Jasinski_, Oct 23 2011