  It is a theorem of Artin, Tits et al. that a finite simple group is
determined by its order, with the exception of the groups (A_3(2), A_2(4)) and
(B_n(q), C_n(q)) for n > 2, q odd. We investigate the situation for finite
semisimple groups of Lie type. It turns out that the order of the finite group
H(F_q) for a split semisimple algebraic group H defined over F_q, does not
determine the group H upto isomorphism, but it determines the field F_q under
some mild conditions.
  We then put a group structure on the pairs (H_1, H_2) of split semisimple
groups defined over a fixed field F_q such that the orders of the finite groups
H_1(F_q) and H_2(F_q) are the same and the groups H_i have no common simple
direct factors. We obtain an explicit set of generators for this abelian,
torsion-free group.
  We finally give a geometric reasoning for these order coincidences.
