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

Author

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

Keywords

• nonn

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).

Examples

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

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

Crossrefs

Cf. A001034, A056866.

Programs

GAP

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