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A051234 Possible orders of central factor groups of groups. 1
1, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contains all even n >= 2, no primes, all prime powers p^n, for n>1. Other entries are complicated and follow from certain congruences.

REFERENCES

Commutativity and Generalizations in Finite Groups, Aine NiShe, Ph.D.thesis in preparation.

LINKS

Table of n, a(n) for n=1..39.

EXAMPLE

a(1)=1,since |G/Z(G)|=1 for all Abelian groups G; a(2)=4,since |Q/Z(Q)|=4 where Q is the quaternion group of order eight.

CROSSREFS

Sequence in context: A077135 A110615 A060679 * A327776 A102554 A070810

Adjacent sequences:  A051231 A051232 A051233 * A051235 A051236 A051237

KEYWORD

nonn,nice,more

AUTHOR

Des MacHale

STATUS

approved

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Last modified October 23 23:06 EDT 2019. Contains 328379 sequences. (Running on oeis4.)