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A212319 The number of abstract groups with minimal permutation representations of degree n. 0

%I

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

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

%C 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.

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

%e 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.

%Y Cf. A174511.

%K nonn,more

%O 1,3

%A _Attila Egri-Nagy_, Oct 25 2013

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)