334 research outputs found
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
Separating cyclic subgroups in graph products of groups
We prove that the property of being cyclic subgroup separable, that is having
all cyclic subgroups closed in the profinite topology, is preserved under
forming graph products.
Furthermore, we develop the tools to study the analogous question in the
pro- case. For a wide class of groups we show that the relevant cyclic
subgroups - which are called -isolated - are closed in the pro- topology
of the graph product. In particular, we show that every -isolated cyclic
subgroup of a right-angled Artin group is closed in the pro- topology, and
we fully characterise such subgroups.Comment: 37 pages, revised following referee's comments, to appear in Journal
of Algebr
Residual properties of automorphism groups of (relatively) hyperbolic groups
We show that Out(G) is residually finite if G is a one-ended group that is
hyperbolic relative to virtually polycyclic subgroups. More generally, if G is
one-ended and hyperbolic relative to proper residually finite subgroups, the
group of outer automorphisms preserving the peripheral structure is residually
finite. We also show that Out(G) is virtually p-residually finite for every
prime p if G is one-ended and toral relatively hyperbolic, or infinitely-ended
and virtually p-residually finite.Comment: v3: as accepted to Geom. & Topol; 29 page
A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable
We prove that the fundamental group of any Seifert 3-manifold is conjugacy
separable. That is, conjugates may be distinguished in finite quotients or,
equivalently, conjugacy classes are closed in the pro-finite topology.Comment: 8 page
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