Re permutation polynomials over a finite field GF(p). It would be nice to characterize the alternating (normal) alternating subgroup of permutation polys. We already know that {x,x+1,1/x} generates full group of perm polys GF(p)(x). {x,x+1,2*x^3} generates alternating subgroup of GF(5)(x). {x,x+1,2*x^5} generates alternating subgroup of GF(7)(x). {x,x+1,3*x^5} generates all of GF(7)(x). Note that x^(p-2) = 1/x, so {x,x+1,2/x} generates alt subgroup of GF(5)(x). {x,x+1,2/x} generates alt subgroup of GF(7)(x). {x,x+1,3/x} generates full group of GF(7)(x). which seems to beg the following conjecture: The alternating subgroup of perm polys of GF(p)(x) is generated by {x,x+1,g/x} when g is NOT a generator of the multiplicative group of GF(p), but instead generates but half of that multiplicative group.