A003788 Order of universal Chevalley group A_n (4).

1, 60, 60480, 987033600, 258492255436800, 1083930404878024704000, 72736898347485916060188672000, 78099458182389588115529148326215680000, 1341733356588640095264385107865053233298800640000

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.
• Index entries for sequences related to groups.

Crossrefs

Cf. A003787, A003789, A003790, A003791, A003792, A053291, A100221.

Programs

Magma

[&*[(4^n - 4^k): k in [0..n-1]]/3: n in [1..8]]; // Vincenzo Librandi, Sep 19 2015

Mathematica

f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}];
f[4, #] & /@ Range[0, 8] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A053291(n)/3. - Ralf Stephan, Mar 30 2004

a(n) = A(4,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

a(n) ~ c * 4^(n*(n+2)), where c = (4/3) * A100221 = 0.918050049493... . - Amiram Eldar, Jul 07 2025

Extensions

One more term from Sean A. Irvine, Sep 18 2015