Noetherian Automorphisms of Groups

An automorphism α of a group G is called a noetherian automorphism if for each ascending chain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ X_1 < X_2 < \ldots < X_n < X_{n + 1} < \ldots $$ \end{document} of subgroups of G there is a positive integer m such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_n^{\alpha} = X_n $$ \end{document} for all n ≥ m. The structure of the group of all noetherian automorphisms of a group is investigated in this paper.