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- Title
On Local Nilpotency of the Normal Subgroups of a Group.
- Authors
Zhang, Zhirang; Li, Jiachao
- Abstract
A group G is said to have property μ whenever N is a non-locally nilpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property ν satisfy property μ, where a group G is said to have property ν if every non-nilpotent normal subgroup of G has a finite non-nilpotent G-quotient. HP(G) is the Hirsch-Plotkin radical of G, and Φf(G) is the intersection of all the maximal subgroups of finite index in G (here Φf(G)=G if no such maximal subgroups exist). It is shown that a group G has property μ if and only if HP(G/Φf(G))=HP(G)/Φf(G) and that the class of groups with property ν is a proper subclass of that of groups with property μ. Also, the structure of the normal subgroups of a group: nilpotency with the minimal condition, is investigated.
- Subjects
NILPOTENT groups; GROUP theory; FINITE groups; SET theory; FRATTINI subgroups
- Publication
Algebra Colloquium, 2016, Vol 23, Issue 3, p531
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386716000511