## 178 Citations

### Isometry types of profinite groups

- Mathematics
- 2008

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.

### Generalized partition functions and subgroup growth of free products of nilpotent groups

- Mathematics
- 2005

Summary We estimate the growth of homomorphism numbers of a torsion-free nilpotent group G using a variant of the circle method together with the analytic continuation of ζG(s) established in [4]. As…

### Counting Subgroups in a Family of Nilpotent Semi‐Direct Products

- Mathematics
- 2004

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…

### A remark on the degree of polynomial subgroup growth of nilpotent groups

- Mathematics
- 2021

We show that if two finitely generated nilpotent groups have isomorphic C-Mal’cev completions, then their subgroup (resp. normal) zeta functions have the same abscissa of convergence. A similar…

### Normal subgroup growth in free class-2-nilpotent groups

- Mathematics
- 2004

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…

### Groups with super-exponential subgroup growth

- MathematicsComb.
- 1996

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

- Mathematics
- 2007

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.

### Analytic properties of Euler products of Igusa-type zeta functions and subgroup growth of nilpotent groups

- Mathematics
- 1999

### Isomorphism Classes and Zeta-functions of Some Nilpotent Groups

- Mathematics
- 2013

. 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

- MathematicsJournal of Mathematical Chemistry
- 2015

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,…

## References

SHOWING 1-10 OF 14 REFERENCES

### The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups

- Mathematics
- 1972

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

- Mathematics
- 1979

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

- MathematicsMathematical 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

- Mathematics
- 1980

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

- Mathematics
- 1971

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

- Mathematics
- 1982

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

- Mathematics
- 1976

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…