On conditions for an endomorphism to be an automorphism

Abstract

If K is a set of automorphisms of a group G, an endomorphism θ : G → G is said to be K-pointwise if for each element t ∈ G, there exists an element φ ∈ K such that θ(t) = φ(t). This generalizes the notion of pointwise inner automorphism. We show that in some special cases, a K-pointwise endomorphism is necessarily an automorphism (it is not true in general). © 2005 AMSS CAS & SUZHOU UNIV.