

A060793


Orders of finite perfect groups (groups such that G = G' where G' is the commutator subgroup of G).


10



1, 60, 120, 168, 336, 360, 504, 660, 720, 960, 1080, 1092, 1320, 1344, 1920, 2160, 2184, 2448, 2520, 2688, 3000, 3420, 3600, 3840, 4080, 4860, 4896, 5040, 5376, 5616, 5760, 6048, 6072, 6840, 7200, 7500, 7560, 7680, 7800, 7920, 9720, 9828, 10080, 10752
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OFFSET

1,2


COMMENTS

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 here all the other numbers are even.
Since a noncyclic simple group is perfect this sequence contains A001034 and since a perfect group is nonsolvable this sequence is a subsequence of A056866 (apart from the initial term).


REFERENCES

D. Holt and W. Plesken, Perfect Groups, Oxford University Press, 1989.


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..300
Walter Feit, J. G. Thompson, A solvability criterion for finite groups and some consequences, Proc. N. A. S. 48 (6) (1962) 968.
Index entries for sequences related to groups


EXAMPLE

A_{5} is perfect since it is equivalent to A_{5}'.


PROG

(GAP) SizesPerfectGroups(); # Eric M. Schmidt, Nov 14 2013


CROSSREFS

Cf. A001034, A056866.
Sequence in context: A096490 A056866 A098136 * A169823 A177871 A252953
Adjacent sequences: A060790 A060791 A060792 * A060794 A060795 A060796


KEYWORD

nonn


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Apr 26 2001


STATUS

approved



