%I A060793
%S A060793 1,60,120,168,336,360,504,660,720,960,1080,1092,1320,1344,1920,2160,2184,
%T A060793 2448,2520,2688,3000,3420,3600,3840,4080,4860,4896,5040,5376,5616,5760,
%U A060793 6048,6072,6840,7200,7500,7560,7680,7800,7920,9720,9828,10080,10752
%N A060793 Orders of finite perfect groups (groups such that G = G' where G' is 
               the commutator subgroup of G).
%C A060793 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 apart from the first trivial term of A060793 all 
               the other numbers in these sequences are even.
%C A060793 Since a non-cyclic simple group is perfect this sequence contains A001034 
               and since a perfect group is non-solvable this sequence is a subsequence 
               of A056866 (apart from the initial term).
%D A060793 D. Holt and W. Plesken, Perfect Groups, Oxford University Press, 1989.
%H A060793 T. Leinster, <a href="http://arXiv.org/abs/math.GR/0104012">Perfect numbers 
               and groups</a>
%e A060793 A_{5} is perfect since it is equivalent to A_{5}'.
%Y A060793 Cf. A001034, A056866.
%Y A060793 Sequence in context: A096490 A056866 A098136 this_sequence A087004 A049058 
               A056501
%Y A060793 Adjacent sequences: A060790 A060791 A060792 this_sequence A060794 A060795 
               A060796
%K A060793 nonn
%O A060793 1,2
%A A060793 Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 26 2001