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A058162
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Number of labeled Abelian groups with a fixed identity.
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6
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1, 1, 1, 4, 6, 60, 120, 1920, 7560, 90720, 362880, 13305600, 39916800, 1037836800, 10897286400, 265547224800, 1307674368000, 66691392768000, 355687428096000, 20274183401472000, 231704953159680000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The distinction here between labeled and unlabeled Abelian groups is analogous to the distinction between unlabeled rooted trees (A000081) and labeled rooted trees (A000169).
That is, the number of Cayley tables. - ARTUR JASINSKI, Mar 12 2008
Number of Latin squares in dimension n with first row and first column 1,2,3 ..., n which are associative and commutative (Abelian). Each of these squares is isomorphic with the Cayley table of one of the existed Abelian group in dimension n. - ARTUR JASINSKI (grafix(AT)csl.pl), Nov 02 2005. Cf. A111341.
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LINKS
| Index entries for sequences related to groups
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EXAMPLE
| The 2 unlabeled Abelian groups of order 4 are C4 and C2^2. The 4 labeled Abelian groups whose identity is "0" consist of 3 of type C4 (where the nongenerator can be "2", "3", or "4") and 1 of type C2^2.
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CROSSREFS
| a(n)=A034382(n)/n. Cf. A000688, A058160, A058161, A058163.
Sequence in context: A012910 A131847 A089630 * A132929 A154668 A189790
Adjacent sequences: A058159 A058160 A058161 * A058163 A058164 A058165
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Nov 15 2000, Mar 12 2008
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