For each k at least 2, the conjugacy growth series of BS(1,k) with respect to the standard generating set is transcendental, and its growth rate equals the standard growth rate.
Rational Growth in Virtually Abelian Groups
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows rationally. These results hold regardless of the choice of finite weighted generating set for $G$.
fields
math.GR 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
The conjugacy growth of the soluble Baumslag-Solitar groups
For each k at least 2, the conjugacy growth series of BS(1,k) with respect to the standard generating set is transcendental, and its growth rate equals the standard growth rate.