A003793 Order of (usually) simple Chevalley group A_n (3).

1, 12, 5616, 6065280, 237783237120, 21032402889738240, 67034222101339041669120, 480860607452861427947598643200, 124190524600592082795473760093457612800

Offset: 0

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

• Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
• Robert Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967, p. 130-131.
• Index entries for sequences related to groups.

Crossrefs

Cf. A003787, A003794, A003795, A003797, A003798, A003799, A100220.

Programs

Mathematica

f[m_, n_] := Block[{g, x, y}, g[x_, y_] := x^(y (y + 1)/2) Product[x^k - 1, {k, 2, y + 1}]; g[m, n]/GCD[n + 1, m - 1]]; f[3, #] & /@ Range[0, 8] (* Michael De Vlieger, Sep 18 2015 *)

Formula

a(n) = a(3,n) where a(q,n) = A(q,n) / gcd(n+1, q-1) and A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

a(n) ~ c * gcd(n, 2) * 3^(n^2 + 2*n), where c = (3/4) * A100220. - Amiram Eldar, Jul 11 2025