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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 (list; graph; refs; listen; history; text; internal format)
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 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 * A169823 A177871 A252953

Adjacent sequences:  A060790 A060791 A060792 * A060794 A060795 A060796

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 20 12:13 EDT 2019. Contains 327231 sequences. (Running on oeis4.)