A003920 Order of universal Chevalley group B_n (3).

24, 51840, 9170703360, 131569513308979200, 152915585868239728626892800, 14395932257291877030764312963579904000, 109777561863482259035023554842176139436811616256000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
• H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Links

• Robert Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967, pp. 130-131.
• Index entries for sequences related to groups.

Crossrefs

Cf. A003921, A003922, A003924, A003925, A003926, A003927, A071302, A132037.

Programs

Mathematica

B[q_, n_] := q^(n^2) * Product[q^(2*k) - 1, {k, 1, n}]; Table[B[3, n], {n, 1, 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). - Sean A. Irvine, Sep 22 2015

a(n) = 2*A003927(n). - Amiram Eldar, Jun 23 2025

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