The proof of Birman's conjecture on singular braid monoids.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
The pseudorational rank of an Abelian group.
The pseudovariety generated by completely 0-simple semigroups.
The pseudovariety is hyperdecidable
The pseudovariety of semigroups of triangular matrices over a finite field
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
The pseudovariety of semigroups of triangular matrices over a finite field
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
The QSF property for groups and spaces.
The quantum duality principle
The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors and , inverse to...
The quasi-uniserial semigroups without zero, their arithmetics and their algebras.
The -free products of archimedean -groups
The objective of this paper is to give two descriptions of the -free products of archimedean -groups and to establish some properties for the -free products. Specifically, it is proved that -free products satisfy the weak subalgebra property.
The range order of a product of i transformations from a finite full transformation semigroup.
The rank of a commutative semigroup
The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups by defining as the supremum of cardinalities of finite independent subsets of . Representing such a semigroup as a semilattice of (archimedean) components , we prove that is the supremum of ranks of various . Representing a commutative separative semigroup as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...
The rank of actions on -trees
The rank of G0 for polycyclic group algebras
The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group
We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.
The ranks of primitive parabolic permutation representations of the simple groups , , and .
The rate of escape for random walks on polycyclic and metabelian groups
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...
The ratio and generating function of cogrowth coefficients of finitely generated groups
Let G be a group generated by r elements . Among the reduced words in of length n some, say , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of has a limit, called the cogrowth exponent with respect to the generators . We show by analytic methods that the numbers vary regularly, i.e. the ratio is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...
The rationality of the Fourier coefficients of certain Eisenstein series on tube domains (I)