Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups
نویسندگان
چکیده
منابع مشابه
Uniform Analytic Properties of Representation Zeta Functions of Finitely Generated Nilpotent Groups
Let G be a finitely generated nilpotent group. The representation zeta function ζG(s) of G enumerates twist isoclasses of finite-dimensional irreducible complex representations of G. We prove that ζG(s) has rational abscissa of convergence α(G) and may be meromorphically continued to the left of α(G) and that, on the line {s ∈ C | Re(s) = α(G)}, the continued function is holomorphic except for ...
متن کاملIsoperimetric Functions of Finitely Generated Nilpotent Groups
We show that the isoperimetric function of a nitely generated nilpotent group of class c is bounded above by a polynomial of degree 2c.
متن کاملDominions in finitely generated nilpotent groups
In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section
متن کاملFinitely generated nilpotent groups are finitely presented and residually finite
Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...
متن کاملZeta functions of nilpotent groups - singular Pfaffians
The local normal zeta functions of a finitely generated, torsion-free nilpotent group G of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in G. The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups w...
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: Transactions of the American Mathematical Society
سال: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6879