On Conditions for an Endomorphism to be an Automorphism

• 来源期刊: 代数集刊（英文版）
• 关键词: endomorphism automorphism soluble group
• 年，卷（期）: 2005,（4）
• 页码范围: 709-714
• 页数: 6页
• 语种: 英文

摘要

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 ψ ∈ K such that θ(t)= ψ(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).