Abstract
1. If P is any property of groups, then we say that a group G is ‘locally P’ if every finitely generated subgroup of G satisfies P. In this paper we shall be chiefly concerned with the case when P is the property of being nilpotent, and will examine some properties of nilpotent groups which also hold for locally nilpotent groups. Examples of locally nilpotent groups are the locally finite p-groups (groups such that every finite subset is contained in a finite group of order a power of the prime p); indeed, every periodic locally nilpotent group is the direct product of locally finite p-groups.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. Soluble and nilpotent groups;Kuroš;Usp. mat. Nauk,1947
2. On Two Questions of Itô
3. On the minimal condition for normal divisors of a locally soluble group;Čarin;Mat. Sborn,1953
4. A note on chain conditions in nilpotent rings and groups
5. Nilpotent groups and their generalizations
Cited by
24 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. New Concepts Related to the Central Series of Lie Rings;Iranian Journal of Science and Technology, Transactions A: Science;2021-11-18
2. Infinite Soluble Groups;A Course in the Theory of Groups;1996
3. Finitary Linear Groups: A Survey;Finite and Locally Finite Groups;1995
4. On groups satisfying the minimal condition on certain subgroups;Periodica Mathematica Hungarica;1983-06
5. Marginal series in groups;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;1977