Virtually free finite-normal-subgroup-free groups are strongly verbally closed
نویسندگان
چکیده
منابع مشابه
The Subgroup Growth Spectrum of Virtually Free Groups
For a finitely generated group Γ denote by μ(Γ) the growth coefficient of Γ, that is, the infimum over all real numbers d such that sn(Γ) < n!d. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. For a finitely generated group Γ denote by sn(Γ) the number of subgroups of inde...
متن کاملFinite automata for Schreier graphs of virtually free groups
The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows an efficient computation of the core of a Schreier graph based on edge folding. It is proved that those groups admitting Stallings sections are precisely f.g. virtually free groups, through a constructive approach based on Basse-Serre theory. Complexity issue...
متن کاملRelative non-Normal Graphs of a Subgroup of Finite Groups
Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...
متن کاملA Subgroup Theorem for Free Products of Pro-Finite Groups
The notion of a free product of pro-finite groups has some important applications in the theory of algebraic number fields (see [3]). In this connection, it is interesting to get some knowledge about the subgroups of such a free product. The aim of this paper is to show a theorem for the open subgroups of a free pro-finite product, which is an analog of Kurosh’s wellknown subgroup theorem for t...
متن کاملNormal subgroup growth in free class-2-nilpotent groups
Let F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions ζ F2,d(s), prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.05.028