[r-t] algebraic theory

[Richard Smith]

Martin Bright wrote:

> for permutation groups (i.e., groups explicitly
> given as subgroups of Sn) it's pretty straightforward: any permutation
> can be written as a product of disjoint cycles, and it's then easy to
> see that the order is the lcm of the lengths of the cycles.  So, in
> S5, if you take a permutation with a 2-cycle and a 3-cycle (say,
> 21534) then the order is 6.  No other combination of cycle lengths can
> do any better.

For the symmetric group, S_n, Landau's function, g(n), gives 
you the maxmimum order of an element.  It has been tabulated 
for n <= 500 000.

   http://mathworld.wolfram.com/LandausFunction.html

RAS