The Recent Generalizations of Colored Symmetry
The Regular Ideal in a Semigroup
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The representation theory and the branching graph for the family of Turaev algebras .
The representations and generic degrees of the Hecke algeba of type H4.
The Residual Finiteness of Certain Amalgameted Free Products.
The residually weakly primitive geometries of .
The Restriction of a Representation of GL2(k) to GL2(o).
The Restriction of Admissible Representations to n.
The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...
The Rhombidodecahedral Tessellation of 3-Space and a Particular 15-Vertex Triangulation of the 3-Dimensional Torus.
The Ribes-Zalesskii property of some one relator groups
The profinite topology on any abstract group , is one such that the fundamental system of neighborhoods of the identity is given by all its subgroups of finite index. We say that a group has the Ribes-Zalesskii property of rank , or is RZ with a natural number, if any product of finitely generated subgroups is closed in the profinite topology on . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ for any natural number . In this paper we characterize groups...
The Riemann theorem and divergent permutations
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series of real terms is rearranged by p to a divergent series . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The ring of quotients of R(S).
The ring of upper triangular invariants as a module over the Dickson invariants.
The role of semigroups in the elementary theory of numbers
The Roquette category of finite -groups
Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges. The main motivation for considering this category is that the additive functors from to...
The Schur Multiplicator of SL(2, Z/mZ) and the Congruence Subgroup Property.
The Schur multiplier of a generalized Baumslag-Solitar group