We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Twisted conjugacy in SL<sub>n</sub> and GL<sub>n</sub> over subrings of ...(t).
- Authors
Mitra, Oorna; Sankaran, Parameswaran
- Abstract
Let φ: G → G be an automorphism of an infinite group G. One has an equivalence relation ~φ on G defined as x ~φ y if there exists a z ∈ G such that y = zxφ(z-1). The equivalence classes are called φ-twisted conjugacy classes, and the set G/~φ of equivalence classes is denoted by R(φ). The cardinality R(φ) of R(φ) is called the Reidemeister number of φ. We write R(φ) = ∞ when R(φ) is infinite. We say that G has the R∞-property if R(φ) = ∞ for every automorphism φ of G. We show that the groups G = GLn(R), SLn(R) have the R∞-property for all n ≥ 3 when F[t] ⊂ R ... F(t), where F is a subfield of Fp. When n ≥ 4, we show that any subgroup H ∈ GLn(R) that contains SLn(R) also has the R∞-property.
- Subjects
INFINITE groups; AUTOMORPHISM groups; CONJUGACY classes; AUTOMORPHISMS; MORPHISMS (Mathematics)
- Publication
Groups, Geometry & Dynamics, 2024, Vol 18, Issue 3, p939
- ISSN
1661-7207
- Publication type
Article
- DOI
10.4171/GGD/758