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SIGMA THEORY AND TWISTED CONJUGACY CLASSES

By Daciberg GONCALVES and Dessislava Hristova KOCHLOUKOVA

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)

Topics: 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
Publisher: PACIFIC JOURNAL MATHEMATICS
Year: 2013
OAI identifier: oai:agregador.ibict.br.RI_UNICAMP:oai:unicamp.sibi.usp.br:SBURI/1097
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