A124900 Largest order of any solvable transitive Galois group for an irreducible polynomial of degree n.

1, 2, 6, 24, 20, 72, 42, 1152, 1296, 800, 110, 82944, 156, 3528, 155520, 7962624, 272, 2239488, 342, 159252480, 11757312, 225280, 506, 13759414272, 64000000, 1277952, 13060694016, 192631799808, 812, 48372940800

Offset: 1

Author

Artur Jasinski, Nov 12 2006

Keywords

• nonn

Comments

These transitive groups are in classification of MAGMA:

a(1)=1T1,a(2)=2T1,a(3)=3T2,a(4)=4T5,a(5)=5T3,a(6)=6T13,

a(7)=7T4,a(8)=8T47,a(9)=9T31,a(10)=10T33,a(11)=11T4,

a(12)=12T294,a(13)=13T6,a(14)=14T45,a(15)=15T87,

a(16)=16T1947,a(17)=17T5,a(18)=18T945,a(19)=19T6,

a(20)=20T1067,a(21)=21T142,a(22)=22T37,a(23)=23T5,

a(24)=24T24921,a(25)=25T179,a(26)=26T79,a(27)=27T2372,

a(28)=28T1773,a(29)=29T6,a(30)=30T5358.

Conjecture: The sequence a(prime(n)), which begins 2, 6, 20, 42, 110, 156, 272, 342, 506, 812, increases without bound. It appears that a(prime(n)) may equal prime(n)(prime(n)-1), which is A036689. - Artur Jasinski, Feb 26 2011

Examples

			a(9)=1296 because solvable Galois group T9_31 (in MAGMA's list) has order 1296
		

Crossrefs

Cf. A099732, A124901, A186772.

Extensions

a(11)-a(30) from Artur Jasinski, Feb 26 2011