A051234 Possible orders of central factor groups of groups.

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

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

Aine NiShe, Commutativity and Generalizations in Finite Groups, 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 A371862

Adjacent sequences: A051231 A051232 A051233 * A051235 A051236 A051237

Keyword

nonn,nice,more

Author

Des MacHale

Status

approved