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

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, 617, 2, 1896, 4

Offset

1,5

Comments

For prime degrees of polynomials see A201443.

All non-solvable groups are non-commutative.

Is this the same as A124938 ? - R. J. Mathar, Oct 04 2018

Links

Table of n, a(n) for n=1..31.

A. Bialostocki and T. Shaska, Galois groups of prime degree polynomials with nonreal roots, 2006.

Example

a(4)=0 because for quartic polynomials all groups are solvable.
a(5)=2 because for quintic polynomials we have two non-solvable groups: A(5) and S(5).

Prog

(Magma) // for a(16):
for g in [1..1954] do
G:=TransitiveGroup(16, g);
IsSolvable(G);
end for

Crossrefs

Cf. A002106, A131932.

Sequence in context: A053049 A306762 A124938 * A081725 A228083 A222234

Adjacent sequences: A198339 A198340 A198341 * A198343 A198344 A198345

Keyword

nonn,hard,more

Author

Artur Jasinski, Oct 23 2011

Status

approved