A212319 The number of abstract groups with minimal permutation representations of degree n.

1, 1, 2, 5, 7, 13, 26, 82, 104, 212, 441, 1171, 1780

Offset: 1

Author

Attila Egri-Nagy, Oct 25 2013

Keywords

• nonn
• more

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.

Examples

			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.

Formula

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