SIGMA THEORY AND TWISTED CONJUGACY CLASSES
Abstract
Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G)- info:eu-repo/semantics/article
- info:eu-repo/semantics/publishedVersion
- Reidemeister class
- Thompson group
- Sigma theory
- automorphism of groups
- R(infinity) property
- limit group
- NEUMANN-STREBEL INVARIANT
- HIGHER GEOMETRIC INVARIANTS
- THOMPSONS GROUP F
- FINITENESS PROPERTIES
- SOLITAR GROUPS
- LIMIT GROUPS
- AUTOMORPHISMS
- VALUATIONS
- PRODUCTS
- BAUMSLAG
- Mathematics