1996/05/17 by Vladimir Shpilrain, Shpilrain, Vladimir
Biochemistry, Genetics and Molecular Biology · Mathematics · #Amino Acid Enzymes and Metabolism #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.math/9605207
LaTex file, 9 pages
arxiv created 1996/05/17 · openalex publication_date 1996/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like an automorphism" on one particular orbit), is itself an automorphism. Then, we consider elements of a different nature, defined by means of homological properties of the corresponding one-relator group. These elements (``generalized primitive elements"), interesting in their own right, can also be used for distinguishing automorphisms among arbitrary endomorphisms.