Twisted Conjugacy Growth of the Generalised Heisenberg Groups

2025/09/02 by Vandeputte, Lukas · 1 citation
#20E45 #20F18 #20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.02231

Abstract

We determine the twisted conjugacy growth function for automorphisms on generalised Heisenberg groups. In particular we demonstrate for these groups that up to a natural equivalence this function is either given by n^k or n^kln(n) for some constant k. We give a precise description for which of these functions we obtain in terms of dimensions and ranks on the upper and lower central series. In particular we obtain that the twisted conjugacy growth is always bounded by the conjugacy growth.

Citations

• Twisted conjugacy growth series of virtually abelian groups
• The twisted conjugacy growth of virtually abelian groups
• Conjugacy growth in the higher Heisenberg groups
• The conjugacy growth of the soluble Baumslag-Solitar groups
• Small cancellations over relatively hyperbolic groups and embedding theorems

Cited by

• Twisted commutativity and conjugacy ratio in groups

Related

• Conjugacy growth in the higher Heisenberg groups
• The twisted conjugacy growth of virtually abelian groups
• Twisted conjugacy growth series of virtually abelian groups
• Twisted commutativity and conjugacy ratio in groups
• Representation growth of the Heisenberg group over O[x]/(xⁿ)