A124938 -id:A124938 - cp's OEIS frontend

A124937 Number of solvable transitive Galois groups for polynomials of degree n.

1, 1, 2, 5, 3, 12, 4, 45, 30, 24, 4, 265, 6, 36, 64, 1905, 5, 892, 6, 759, 108, 32, 4, 24193, 132, 70, 2328, 1237, 6, 3816, 8

Offset: 1

Artur Jasinski, Nov 13 2006

			a(5) = 3: for polynomials of degree 5 we have 3 solvable groups: C5 (T5_1), D5 (T5_2) and F5(T5_3)

Bialostocki A. & Shaska T., Galois groups of prime degree polynomials with nonreal roots. arXiv:math/0601397

Cf. A002106, A124938.

"a(15)= "; l:=AllTransitiveGroups(NrMovedPoints,15,IsSolvable,true); # Artur Jasinski, Feb 04 2007

// a(10)
for g in [1..45] do
G:=TransitiveGroup(10,g);
IsSolvable(G);
end for;

More terms from Artur Jasinski, Feb 04 2007

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

Original entry on oeis.org

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

Artur Jasinski, Oct 23 2011

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

			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).

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

Cf. A002106, A131932.

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

cp's OEIS Frontend

A124937 Number of solvable transitive Galois groups for polynomials of degree n.

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