I was just looking at the code for multiplicative_order in
finite_field_element.py, and noticed that it factors the group order,
and find the "cofactors" corresponding to each prime power dividing
the order (which is really the only algorithm that I know to do
this).  To avoid repeating this calculation for elements of finite
fields it would be nice if the finite field could cache this
information, so that it wouldn't have to be recalculated.  The same
remark should hold for finite abelian groups (since it's really the
same algorithm).

Victor
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