[GAP Forum] A permutation group with huge finite orbits

[Bill Allombert]

On Mon, Nov 19, 2012 at 05:05:42PM -0000, Stefan Kohl wrote:
> Proving finiteness of all cycles may be pretty hard, however.

Indeed, this problem is too close to the Collatz ((3n+1)/2) conjecture
for comfort.

The Collatz sequence can be restated in your notation by
asking whether the orbits of Z under M are finite, where M is the submonoid 
of Z^Z generated by a = (1(2)->2(3)) and b = (0(2)->0(1)) 
(a and b are not one-to-one).

Cheers,
Bill.