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

@inproceedings{Sulca2021ARO, title={A remark on the degree of polynomial subgroup growth of nilpotent groups}, author={Diego Sulca}, year={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 result is formulated and proved for zeta functions of finitely generated virtually nilpotent groups.

## One Citation

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## References

SHOWING 1-10 OF 20 REFERENCES

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…

Finitely generated groups of polynomial subgroup growth

- Mathematics
- 1993

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.

Zeta functions of integral nilpotent quiver representations

- Mathematics
- 2020

We introduce and study zeta functions enumerating subrepresentations of integral quiver representations. For nilpotent such representations defined over number fields, we exhibit a homogeneity…

Computing local zeta functions of groups, algebras, and modules

- Mathematics
- 2016

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local…

Zeta functions of groups and rings

- Mathematics
- 2007

We report on progress and problems concerning the analytical behaviour of the zeta
functions of groups and rings. We also describe how these generating functions are special cases
of adelic cone…

Rational forms of nilpotent Lie algebras and Anosov diffeomorphisms

- Mathematics
- 2008

Abstract.We compute the set of all rational forms up to isomorphism for some real nilpotent Lie algebras of dimension 8. This is part of the classification of nilmanifolds admitting an Anosov…

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…

Analytic properties of zeta functions and subgroup growth

- Mathematics
- 2000

It has become somewhat of a cottage industry over the last fifteen years to understand the rate of growth of the number of subgroups of finite index in a group G. Although the story began much…

Subgroup growth of lattices in semisimple Lie groups

- Mathematics
- 2004

We give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie groups. In the most…