Abstract
Let u(x1,…,xn) = x11 … x1m be a word in the alphabet x1, …,xn such that x1i ≠ x1i for all i = 1,…, m − 1. If (H1, …, Hn) is an n-tuple of subgroups of a group G then denote by u(H1, …, Hn) the set {u(h1,…,hn) | hi ∈ Hi}. If σ ∈ Sn then denote by uσ(H1,…,Hn) the set u(Hσ(1),…,Hσ(n)). We study groups G with the property that for each n-tuple (H1,…,Hn) of subgroups of G, there is some σ ∈ Sn σ ≠ 1 such that u(H1,…,Hn) = uσ(H1,…,Hn). If G is a finitely generated soluble group then G has this property for some word u if and only if G is nilpotent-by-finite. In the paper we also look at some specific words u and study the properties of the associated groups.
Publisher
Cambridge University Press (CUP)
Reference9 articles.
1. Additive relations in number fields;Van der Poorten;Séminaire de Théorie des Nombres de Paris,1982
2. [5] Longobardi P. , Maj M. and Rhemtulla A.H. , ‘Periodic groups with, permutable subgroup products’, Math. Proc. Cambridge Philos. Soc. (to appear).
3. [8] Smith H. , ‘Elliptically embedded subgroups and nilpotent products’. (submitted).
4. Rewriting products of group elements—I
5. Groups with Representations of Bounded Degree
Cited by
2 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