A060793 Orders of finite perfect groups (groups such that G = G' where G' is the commutator subgroup of G).

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

Offset

1,2

Comments

This comment is about the three sequences A001034, A060793, A056866: 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 [Corrected by Isaac Saffold, Aug 09 2021]

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).

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 * A371037 A334761 A169823

Adjacent sequences: A060790 A060791 A060792 * A060794 A060795 A060796

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 26 2001

Status

approved