Baumslag-Solitar groups and some other groups of cohomological dimension two.
Bemerkung zu der Arbeit: „Die Anwendung der Polarität auf die direkten Produktzerlegungen einer Gruppe‟ von František Šik
Berichtigung zu der Arbeit "Gleichungen in freien Produkten mit Amalgan".
Bicartesian Squares of Nilpotent Groups.
Bicyclic commutator quotients with one non-elementary component
For any number field with non-elementary -class group , , the punctured capitulation type of in its unramified cyclic cubic extensions , , is an orbit under the action of . By means of Artin’s reciprocity law, the arithmetical invariant is translated to the punctured transfer kernel type of the automorphism group of the second Hilbert -class field of . A classification of finite -groups with low order and bicyclic commutator quotient , , according to the algebraic invariant...
Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.
Boundaries of right-angled hyperbolic buildings
We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.
Bounded, separating, incompressible surfaces in knot manifolds.
Bounding the complexity of simplicial group actions on trees.
Bounding the orders of finite subgroups.
We give homological conditions on groups such that whenever the conditions hold for a group G, there is a bound on the orders of finite subgroups of G. This extends a result of P. H. Kropholler. We also suggest a weaker condition under which the same conclusion might hold.
Breaking points in the poset of conjugacy classes of subgroups of a finite group
We determine the finite groups whose poset of conjugacy classes of subgroups has breaking points. This leads to a new characterization of the generalized quaternion -groups. A generalization of this property is also studied.
Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings
We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group over a suitable non-Archimedean field we define a map from the Bruhat-Tits building to the Berkovich analytic space associated with . Composing this map with the projection of to its flag varieties, we define a family of compactifications of . This generalizes results by Berkovich in the case of split groups. Moreover,...
Brunnian links
A Brunnian link is a set of n linked loops such that every proper sublink is trivial. Simple Brunnian links have a natural algebraic representation. This is used to determine the form, length and number of minimal simple Brunnian links. Braids are used to investigate when two algebraic words represent equivalent simple Brunnian links that differ only in the arrangement of the component loops.
Buildings and non-positively curved polygons of finite groups.
Calculating the genus of a direct product of certain nilpotent groups.
The Mislin genus G(N) of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. If N satisfies some additional conditions -we say that N belongs to N1- we know exactly the structure of G(N). Considering a direct product N1 x ... x Nk of groups in N1 takes us virtually always out of N1. We here calculate the Mislin genus of such a direct product.
Calculation of Baer-invariant of Certain Groups.
Canonical bases for normal subgroups of finitely generated free groups with finite abelian factor groups.
Caratterizzazione dei gruppi immagini omomorfe duali di un gruppo finito
Carter subgroups and injectors in a class of locally finite groups
...-Categorical Stable Groups.