Twisted conjugacy in and over subrings of
Oorna Mitra
Chennai Mathematical Institute, Kelambakkam, India; Indian Statistical Institute, Bengaluru, IndiaParameswaran Sankaran
Chennai Mathematical Institute, Kelambakkam, India
![Twisted conjugacy in $\mathrm{SL}_{n}$ and $\mathrm{GL}_{n}$ over subrings of $\overline{\mathbb{F_p}}(t)$ cover](/_next/image?url=https%3A%2F%2Fcontent.preview.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-18-issue-3.png&w=3840&q=90)
Abstract
Let be an automorphism of an infinite group . One has an equivalence relation on defined as if there exists a such that . The equivalence classes are called -twisted conjugacy classes, and the set of equivalence classes is denoted by . The cardinality of is called the Reidemeister number of . We write when is infinite. We say that has the -property if for every automorphism of . We show that the groups have the -property for all when , where is a subfield of . When , we show that any subgroup that contains also has the -property.
Cite this article
Oorna Mitra, Parameswaran Sankaran, Twisted conjugacy in and over subrings of . Groups Geom. Dyn. 18 (2024), no. 3, pp. 939–962
DOI 10.4171/GGD/758