|
|
A198342
|
|
Number of non-solvable transitive permutation groups for polynomials of degree n.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
For prime degrees of polynomials see A201443.
All non-solvable groups are non-commutative.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|