Search: id:A124827
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%I A124827
%S A124827 1,2,6,8,20,12,42,16,54,40,110,48,156,84,120,64,272,108,342,160,252
%N A124827 Order of Galois groups of irreducible Chebyshev polynomials of order 
               n.
%C A124827 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
%e A124827 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.
%o A124827 (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 
               //
%Y A124827 Cf. A001710, A000142, A036689.
%Y A124827 Cf. A127835.
%Y A124827 Sequence in context: A106164 A072230 A028332 this_sequence A140965 A002618 
               A069553
%Y A124827 Adjacent sequences: A124824 A124825 A124826 this_sequence A124828 A124829 
               A124830
%K A124827 nonn,uned
%O A124827 1,2
%A A124827 Artur Jasinski (grafix(AT)csl.pl), Nov 09 2006

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