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Search: id:A051234
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| A051234 |
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Possible orders of central factor groups of groups. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Contains all even n >= 2, no primes, all prime powers p^n, for n>1. Other entries are complicated and follow from certain congruences.
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REFERENCES
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Commutativity and Generalizations in Finite Groups, Aine NiShe, Ph.D.thesis in preparation.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A077135 A110615 A060679 this_sequence A102554 A090419 A070810
Adjacent sequences: A051231 A051232 A051233 this_sequence A051235 A051236 A051237
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KEYWORD
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nonn,nice
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AUTHOR
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Des MacHale (stmt8011(AT)bureau.ucc.ie)
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