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A124827
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Order of Galois groups of irreducible Chebyshev polynomials of order n.
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3
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1, 2, 6, 8, 20, 12, 42, 16, 54, 40, 110, 48, 156, 84, 120, 64, 272, 108, 342, 160, 252
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OFFSET
| 1,2
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COMMENTS
| All groups belonging to solvable Galois groups. Very similar sequence is A002618 (disagreement occured only for Chebyshev polynomials orders 8 and 16) When order of non-reducible Chebyshev polynomial n is prime number Galois group is Froebenius group of order n*(n-1) A036689 In MAGMA classification the Galois groups are the following: T1_1, T2_1, T3_2, T4_3, T5_3, T6_3, T7_4, T8_8, T9_10, T11_4, T12_28, T13_6, T14_7, T15_11, T16_144, T17_5, T18_45, T19_6, T20_42, T21_15
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EXAMPLE
| a(5)=20 because order of Galois group of polynomial 16x^5-20x^3+5x-c is 20 (where c is an integer chosen so that the polynomial is irreducible). This transitive group is the Frobenius group F5 of order 20 (also called the metacyclic group M_5) T5_3(20) in MAGMA classification.
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PROG
| (MAGMA) Zx<x>:=PolynomialRing(Integers()); f:=16*x^5-20*x^3+5*x-7; G:=GaloisGroup(f:Old); "Order of group", #G; // *author: Juergen Klueners klueners(AT)math.uni-duesseldorf.de //
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CROSSREFS
| Cf. A001710, A000142, A036689.
Cf. A127835.
Sequence in context: A072230 A028332 A183171 * A140965 A002618 A069553
Adjacent sequences: A124824 A124825 A124826 * A124828 A124829 A124830
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KEYWORD
| nonn,uned
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Nov 09 2006
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