So it's been suggested ( see the discussion of 
https://github.com/sympy/sympy/pull/1319
) that we get rid of the slightly long Permutation and replace it with
the shorter Perm in sympy/combinatorics/permutations.py. Keeping with
this, we should also rename PermutationGroup to PermGroup in sympy/
combinatorics/perm_groups.py. It sounds like a good idea to me. Are
there any objections to that?

Also, there was a discussion about the checks that are performed every
time we construct a Permutation object - whether all numbers from 0 to
n-1 are present and the arguments provided are the way they should be.
They tend to greatly slow down the construction of a Permutation
object; on the other hand, it might be helpful to keep them in order
to quickly spot if you're doing something stupid. And there are fast
factory functions for constructing permutations that skip these
checks, like new_from_array_form. But it seems that users might also
want to skip the checks if they know what they're doing and are
working with permutations of sizes in the millions.

So, do you have any suggestions about what we should do, keep the
checks, remove them, or something in between?

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