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A212319 The number of abstract groups with minimal permutation representations of degree n. 0
1, 1, 2, 5, 7, 13, 26, 82, 104, 212, 441, 1171, 1780 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) can be derived by setting a(1)=1 and then taking the differences between the consecutive elements of A174511. This is due to the fact that if an abstract group can be represented as a permutation group on n points, then it can also be represented by a permutation group of degree n+1, simply by including a fixed point. In other words, the sum of the first n terms give you the number of isomorphism classes of subgroups of the symmetric group of degree n.

LINKS

Table of n, a(n) for n=1..13.

FORMULA

a(1)=1, a(n) =  A174511(n) -  A174511(n-1), n>1.

EXAMPLE

a(1)=1, since only the trivial group 1 can be represented as permutations of a single point. a(2)=1 because Z_2,1 can both be realized by permutations of two points but for 1 this representation is not minimal. a(3)=2 with Z_3 and S_3 appearing for the first time.

CROSSREFS

Cf. A174511.

Sequence in context: A155028 A119839 A107057 * A161379 A250173 A038945

Adjacent sequences:  A212316 A212317 A212318 * A212320 A212321 A212322

KEYWORD

nonn,more

AUTHOR

Attila Egri-Nagy, Oct 25 2013

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)