382 research outputs found
Conjugacy Growth and Conjugacy Width of Certain Branch Groups
The conjugacy growth function counts the number of distinct conjugacy classes
in a ball of radius . We give a lower bound for the conjugacy growth of
certain branch groups, among them the Grigorchuk group. This bound is a
function of intermediate growth. We further proof that certain branch groups
have the property that every element can be expressed as a product of uniformly
boundedly many conjugates of the generators. We call this property bounded
conjugacy width. We also show how bounded conjugacy width relates to other
algebraic properties of groups and apply these results to study the palindromic
width of some branch groups.Comment: Final version, to appear in IJA
Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary
This is the third in a series of papers constructing hyperbolic structures on
all Haken three-manifolds. This portion deals with the mixed case of the
deformation space for manifolds with incompressible boundary that are not
acylindrical, but are more complicated than interval bundles over surfaces.
This is a slight revision of a 1986 preprint, with a few figures added, and
slight clarifications of some of the text, but with no attempt to connect this
to later developments such as groups acting on R-trees, etc.Comment: 19 pages, 4 figure
Profinite Groups and Discrete Subgroups of Lie Groups
[no abstract available
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