[r-t] algebraic theory
Richard Smith
richard at ex-parrot.com
Thu Jan 31 11:21:43 UTC 2013
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
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