Blocks with Dihedral Defect Groups in Solvable Groups.
Bol loop actions.
Bol loop actions
The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99].
Bol loops with a large left nucleus
Possession of a unique nonidentity commutator/associator is a property which dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an ``interesting'' identity. Indeed, until now, with the exception of some ad hoc examples, the only known class of Bol loops whose loop rings satisfy the right Bol identity have this property. In this paper, we identify another class of loops whose loop rings are ``strongly right alternative'' and present various constructions of...
Bol-loops of order
In this article we construct proper Bol-loops of order using a generalisation of the semidirect product of groups defined by Birkenmeier and Xiao. Moreover we classify the obtained loops up to isomorphism.
Boolean groupoids
Bootstrapping in convergence groups.
Borders and roots of a word
Borel semigroups and probabilities.
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 Baer-Levi semigroups.
Bounded cohomology of lattices in higher rank Lie groups
We prove that the natural map from bounded to usual cohomology is injective if is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for : the stable commutator length vanishes and any –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating to the continuous bounded cohomology of the ambient group...
Bounded derivations on commutative semigroups.
Bounded generation and Kazhdan’s property
Bounded generation of (after D. Carter, G. Keller, and E. Paige).
Bounded geometry in relatively hyperbolic groups.
Bounded, separating, incompressible surfaces in knot manifolds.
Bounding the complexity of simplicial group actions on trees.
Bounding the number of edges in permutation graphs.
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.