Geodesic growth in virtually abelian groups

نویسندگان

چکیده

We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and series holonomic, rational in case. In addition, we language geodesics blind multicounter.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Regular geodesic normal forms in virtually abelian groups

We describe a virtually abelian group G generated by a nite set X such that there is no regular language of geodesic X-words that surjects to G by evaluation.

متن کامل

Groups whose proper quotients are virtually abelian

The just non-(virtually abelian) groups with non-trivial Fitting subgroup are classified. Particular attention is given to those which are virtually nilpotent and examples are given of the interesting phenomena that can occur.

متن کامل

Closed BLD-elliptic manifolds have virtually Abelian fundamental groups

We show that a closed, connected, oriented, Riemannian n-manifold, admitting a branched cover of bounded length distortion from R, has a virtually Abelian fundamental group.

متن کامل

Hyperelementary Induction for K-theory of Virtually Abelian Groups

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group.

متن کامل

JSJ-Decompositions of Coxeter Groups over Virtually Abelian Splittings

The idea of “JSJ-decompositions” for 3-manifolds began with work of Waldhausen and was developed later through work of Jaco, Shalen and Johansen. It was shown that there is a finite collection of 2-sided, incompressible tori that separate a closed irreducible 3-manifold into pieces with strong topological structure. Sela introduced the idea of JSJ-decompositions for groups, an idea that has flo...

متن کامل

ذخیره 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: 2021

ISSN: ['1090-266X', '0021-8693']

DOI: https://doi.org/10.1016/j.jalgebra.2020.12.003