A131932 -id:A131932 - cp's OEIS frontend

A131933 a(n) = A056866(n)/4.

15, 30, 42, 45, 60, 75, 84, 90, 105, 120, 126, 135, 150, 165, 168, 180, 195, 210, 225, 240, 252, 255, 270, 273, 285, 294, 300, 315, 330, 336, 345, 360, 375, 378, 390, 405, 420, 435, 450, 462, 465, 480, 495, 504, 510, 525, 540, 546, 555, 570, 585, 588, 600, 612

Offset: 1

Artur Jasinski, Jul 30 2007

nonn

All orders of nonsolvable groups A056866 are divisible by 4.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001034, A060793, A056866, A056868, A131932.

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

A201443 Number of non-solvable transitive permutation groups for polynomials of degree p(n), where p(n) is n-th prime.

Original entry on oeis.org

0, 0, 2, 3, 4, 3, 5, 2, 3, 2, 4

Offset: 1

Artur Jasinski, Dec 01 2011

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

Cf. A002106, A131932, A198342.

A231867 Number of perfect groups of order A060793(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 5, 1, 1, 3, 1, 1, 9, 4, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 5, 22, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 37, 2, 1, 1, 4, 1, 1, 1, 4, 25, 3, 1, 1, 1, 3, 1

Offset: 1

Eric M. Schmidt, Nov 14 2013

nonn

Cf. A131932.

A231867 := n -> NrPerfectGroups(SizesPerfectGroups()[n]); # works for most n <= 331.

cp's OEIS Frontend

A131933 a(n) = A056866(n)/4.

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

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Magma

A201443 Number of non-solvable transitive permutation groups for polynomials of degree p(n), where p(n) is n-th prime.

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A231867 Number of perfect groups of order A060793(n).

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Programs

GAP