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- Title
On finite 2-equilibrated p-groups.
- Authors
Jiao Wang; Xiuyun Guo
- Abstract
A finite group G is said to be n-equilibrated if, for all subgroups H and K of G with d(H) ≥ n and d(K) ≥ n, either H ≤ NG(K) or K ≤ NG(H). In this paper, we investigate the structure of finite 2-equilibrated p-groups G. We provide a complete classification of such groups when G is 2-generator. If G is 3-generator, we prove that G has a normal metacyclic subgroup N such that G/N is cyclic and, if G has at least four generators, we prove that G is modular and G' ≤ 〈x〉 for any element x in G with o(x) D exp(G).
- Subjects
FINITE element method; ALGEBRA; ELECTRIC generators; GROUP theory; FINITE groups
- Publication
Journal of Group Theory, 2016, Vol 19, Issue 4, p569
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2015-0042