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Abstract: In this paper, we consider the conjugacy growth function of a group, whichcounts the number of conjugacy classes which intersect a ball of radius $n$centered at the identity. We prove that in the case of virtually polycyclicgroups, this function is either exponential or polynomially bounded, and ispolynomially bounded exactly when the group is virtually nilpotent. The proofis fairly short, and makes use of the fact that any polycyclic group has asubgroup of finite index which can be embedded as a lattice in a Lie group, aswell as exponential radical of Lie groups and Dirichlet-s approximationtheorem.



Author: M. Hull

Source: https://arxiv.org/







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