Texas A&M University, Department of
Mathematics, 216 Milner Hall, 21st of February 2007, 3:00-3:50
Groups and Dynamics Seminar
Reidemeister
numbers of saturated weakly branch groups
Evgeny Troitskiy of Moscow State
University, Russia
A group G with the property that, for every automorphism f of G, the
Reidemeister number R(f) is infinite are said to have the R-infinity
property. In particular, the twisted Burnside-Frobenius Theorem
(discussed in the previous talk) does not apply to such groups (the
presentation will be independent on the previous talk and needs no
Functional Analysis).
After presenting some known cases we concentrate on saturated weakly
branch groups and prove that all groups in a wide class of saturated
weakly branch groups (including Grigorchuk group and Gupta-Sidki group)
have the R-infinity property.
(joint work with A. Felshtyn and Yu. Leonov)