The Reidemeister Spectra of Low Dimensional Almost-Crystallographic Groups

Abstract

We determine which non-crystallographic, almost-crystallographic groups of dimension-4 have the R_∞-property. We then calculate the Reidemeister spectra of the 3-dimensional almost-crystallographic groups and the 4-dimensional almost-Bieberbach groups.

Keywords:

• group theory
• fixed point theory
• almost-crystallographic group
• automorphism
• Nielsen fixed point theory

Acknowledgment

The author would like to thank the referee for their careful reading and useful suggestions for the article.

Additional information

Funding

This work was supported by long-term structural funding—Methusalem grant of the Flemish Government.