Generalized primitive elements of a free group
群论
2008-02-03 v1
摘要
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.
引用
@article{arxiv.math/9605207,
title = {Generalized primitive elements of a free group},
author = {Vladimir Shpilrain},
journal= {arXiv preprint arXiv:math/9605207},
year = {2008}
}
备注
LaTex file, 9 pages