A003927 Order of simple Chevalley group B_n (3).

25920, 4585351680, 65784756654489600, 76457792934119864313446400, 7197966128645938515382156481789952000, 54888780931741129517511777421088069718405808128000

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Index entries for sequences related to groups.

Crossrefs

Cf. A003920, A003938, A003939, A003940, A003941, A003942, A132037.

Programs

Mathematica

b[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}] / GCD[2, q-1]; Table[b[3, n], {n, 2, 7}] (* Amiram Eldar, Jun 23 2025 *)

Formula

a(n) = b(3,n) where b(q,n) = q^(n^2) * Product_{k=1..n}(q^(2*k)-1) / gcd(2, q-1). - Sean A. Irvine, Sep 22 2015

a(n) = A003920(n) / 2. - Amiram Eldar, Jun 23 2025

a(n) ~ c * 3^(2*n^2+n), where c = A132037. - Amiram Eldar, Jul 09 2025