Inverse ambiguous functions and automorphisms on finite groups - Toborg, Imke (Annales Mathematicae Silesianae, 2019)
If G is a finite group, then a bijective function f:G→G is inverse ambiguous if and only if f(x)-1 = f-1(x) for all x∈G. We give a precise description when a finite group admits an inverse ambiguous function and when a finite group admits an inverse ambiguous automorphism.