Subgroups of finite index in nilpotent groups

  title={Subgroups of finite index in nilpotent groups},
  author={Fritz Grunewald and Dan Segal and G. C. Smith},
  journal={Inventiones mathematicae},

Isometry types of profinite groups

Let T be a rooted tree and Iso(T) be the group of its isometries. We study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.

Counting Subgroups in a Family of Nilpotent Semi‐Direct Products

In this paper we compute the subgroup zeta functions of nilpotent groups of the form Gn:=〈x1,…,xn,y1,…,yn−1∣[xi,xn]=yi,1⩽i⩽n−1 , all other [,] trivial 〉 and deduce local functional equations. 2000

Normal subgroup growth in free class-2-nilpotent groups

Abstract.Let F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions prove that they satisfy local functional equations and determine their abscissae of

Normal Zeta Functions of Some pro-p Groups

We give an explicit formula for the number of normal subgroups of index p n of the pro-p group , and for the normal zeta function associated with this group. Let 𝒬1(s, r) be the subgroups of the

Groups with super-exponential subgroup growth

It is shown that, if the subgroup growth of a finitely generated groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG.

On the degree of polynomial subgroup growth in class 2 nilpotent groups

We use the theory of zeta functions of groups to establish a lower limit for the degree of polynomial normal subgroup growth in class two nilpotent groups.

Isomorphism Classes and Zeta-functions of Some Nilpotent Groups

. In this article, we study a class of groups which are commensurable with a direct product of the discrete Heisenberg group and a free abelian group, or a free abelian group by using zeta functions

Zeta and normal zeta functions for a subclass of space groups

We calculate zeta and normal zeta functions of space groups with the point group isomorphic to the cyclic group of order 2. The obtained results are applied to determine the number of subgroups,

Finitely generated groups of polynomial subgroup growth

We determine the structure of finitely generated residually finite groups in which the number of subgroups of each finite indexn is bounded by a fixed power ofn.



The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups

It will be convenient to say that a group G virtually has a property P if some subgroup of finite index has property P. Thus the theorem above concludes that 'G is virtually nilpotent'. (This

Symmetric functions and Hall polynomials

I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions

On the automorphism groups of certain Lie algebras

  • D. Segal
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1989
We fix a ground field k and a finite separable extension K of k. To a Lie algebra L over k is associated the Lie algebra KL = K ⊗kL over K. If we forget the action of K, we can think of KL as a

Solomon's conjectures and the local functional equation for zeta functions of orders

p and introduced a "global" zeta function fA(s), which depends on A and R but not on A, with the property that the P-part of ÇA(s) coincides with ?AJ>() f° r almost all P. (To be explicit, this

Finitely generated nilpotent groups with isomorphic finite quotients

Let Y(G) denote the set of isomorphism classes of finite homomorphic images of a group G. We say that groups G and H have isomorphic finite quotients if Y(G)=Y(H). In this paper we show that if G is

Adeles and algebraic groups

I. Preliminaries on Adele-Geometry.- 1.1. Adeles.- 1.2. Adele-spaces attached to algebraic varieties.- 1.3. Restriction of the basic field.- II. Tamagawa Measures.- 2.1. Preliminaries.- 2.2. The case

Modular Functions and Dirichlet Series in Number Theory

This is the second volume of a 2-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume