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

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

Offset

0,2

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, 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

Table of n, a(n) for n=0..8.

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

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

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 *)

Crossrefs

Sequence in context: A229669 A013508 A230749 * A171669 A094268 A208865

Adjacent sequences: A003790 A003791 A003792 * A003794 A003795 A003796

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved