743 research outputs found
On Residual Properties of Word Hyperbolic Groups
For a fixed word hyperbolic group we compare different residual properties
related to quasiconvex subgroups.Comment: 17 pages. Final version: several typos correcte
New examples of groups acting on real trees
We construct the first example of a finitely generated group which has
Serre's property (FA) (i.e., whenever it acts on a simplicial tree it fixes a
vertex), but admits a fixed point-free action on an -tree with
finite arc stabilizers. We also give a short and elementary construction of
finitely generated groups that have property (FA) but do not have
(F).Comment: v4: 22 pages, revised following referee's suggestions. This version
of the paper has been accepted by the Journal of Topolog
Hereditary conjugacy separability of right angled Artin groups and its applications
We prove that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group contains a conjugacy separable subgroup of finite index and has a residually finite outer automorphism group. Another consequence of the main result is that Bestvina-Brady groups are conjugacy separable and have solvable conjugacy proble
On subgroups of right angled Artin groups with few generators
For each natural number we construct a -generated group , which
is a subdirect product of free groups, such that the cohomological dimension of
is . Given a group and a normal subgroup we prove that
any right angled Artin group containing the special HNN-extension of with
respect to must also contain . We apply this to construct, for every
, a -generated group , embeddable into a right angled
Artin group, such that the cohomological dimension of is but the
cohomological dimension of any right angled Artin group, containing , is
at least . These examples are used to show the non-existence of certain
"universal" right angled Artin groups.
We also investigate finitely presented subgroups of direct products of limit
groups. In particular we show that for every there exists
such that any -generated finitely presented
subgroup of a direct product of finitely many free groups embeds into the
-th direct power of the free group of rank . As another corollary
we derive that any -generated finitely presented residually free group
embeds into the direct product of at most limit groups.Comment: v4: accepted in this format for publication in Intern. J. Algebra and
Comput.; 12 page
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