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 A001034 Orders of non-cyclic simple groups (without repetition). (Formerly M5318 N2311) 18

%I M5318 N2311

%S 60,168,360,504,660,1092,2448,2520,3420,4080,5616,6048,6072,7800,7920,

%T 9828,12180,14880,20160,25308,25920,29120,32736,34440,39732,51888,

%U 58800,62400,74412,95040,102660,113460,126000,150348,175560,178920

%N Orders of non-cyclic simple groups (without repetition).

%C This comment is about the four sequences A001034, A060793, A056866, A056868: The Feit-Thompson theorem says that a finite group with odd order is solvable, hence all numbers in this sequence are even. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 08 2001

%C The primitive elements are A257146. These are also the primitive elements of A056866. - _Charles R Greathouse IV_, Jan 19 2017

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.

%D Dickson L.E. Linear groups, with an exposition of the Galois field theory (Teubner, 1901), p. 309.

%D M. Hall, Jr., A search for simple groups of order less than one million, pp. 137-168 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David A. Madore, <a href="/A001034/b001034.txt">Table of n, a(n) for n = 1..491</a> [taken from link below]

%H C. Cato, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0430052-X">The orders of the known simple groups as far as one trillion</a>, Math. Comp., 31 (1977), 574-577.

%H L. E. Dickson, <a href="http://cdl.library.cornell.edu/Hunter/hunter.pl?handle=cornell.library.math/05110001&amp;id=5">Linear Groups with an Exposition of the Galois Field Theory</a> (page images), Dover, NY, 1958, p. 309.

%H Walter Feit, J. G. Thompson, <a href="http://www.pnas.org/content/48/6/968">A solvability criterion for finite groups and some consequences</a>, Proc. N. A. S. 48 (6) (1962) 968

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%H <a href="/index/Cor#core">Index entries for "core" sequences</a>

%Y Cf. A000001, A000679, A005180, A001228, A060793, A056866, A056868, A119630.

%Y Cf. A109379 (orders with repetition), A119648 (orders that are repeated).

%K nonn,nice,core

%O 1,1

%A _N. J. A. Sloane_, _Simon Plouffe_

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Last modified September 25 01:17 EDT 2018. Contains 315360 sequences. (Running on oeis4.)