[r-t] Decisions / Algorithms for generating the extent

[Martin Bright]

Richard Smith:

> Suppose for n>3 it can be done with two changes a and b.
> Clearly the extent has to be of the form ababababab... as
> two consecutive instances of the same change would
> immediately be false.  This means that the touch will be
> twice the order of the permutation ab.

To finish this off more quickly, just observe that Sn doesn't have any
cyclic subgroups of index 2 (when n > 3).

Martin