On conjugacy growth for solvable groups
Emmanuel Breuillard, Yves de Cornulier

TL;DR
This paper proves that finitely generated solvable groups that are not virtually nilpotent exhibit exponential growth in the number of conjugacy classes as their elements grow larger.
Contribution
It establishes a clear dichotomy in conjugacy growth behavior for solvable groups based on their nilpotency properties.
Findings
Finitely generated solvable non-virtually nilpotent groups have exponential conjugacy growth.
Virtually nilpotent solvable groups do not necessarily have exponential conjugacy growth.
Provides a classification criterion based on conjugacy growth for solvable groups.
Abstract
We prove that a finitely generated solvable group which is not virtually nilpotent has exponential conjugacy growth.
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