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Displaying 521 – 540 of 859

The ratio and generating function of cogrowth coefficients of finitely generated groups

Ryszard Szwarc (1998)

Studia Mathematica

Let G be a group generated by r elements $g_{1}, \dots, g_{r}$ . Among the reduced words in $g_{1}, \dots, g_{r}$ of length n some, say $γ_{n}$ , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of $γ_{2 n}$ has a limit, called the cogrowth exponent with respect to the generators $g_{1}, \dots, g_{r}$ . We show by analytic methods that the numbers $γ_{n}$ vary regularly, i.e. the ratio $γ_{2 n + 2} / γ_{2 n}$ 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)

Liang-Chi Tsao (1976)

Compositio Mathematica

The real genus of the alternating groups.

J. J. Etayo Gordejuela, E. Martínez (2008)

Revista Matemática Iberoamericana

The Recent Generalizations of Colored Symmetry

Lungu Alexandru (2000)

Visual Mathematics

The Regular Ideal in a Semigroup

Harbans Lal (1975)

Matematický časopis

The relationship between Zhedanov's algebra $A W (3)$ and the double affine Hecke algebra in the rank one case.

Koornwinder, Tom H. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The representation theory and the branching graph for the family of Turaev algebras ${H_{q}^{1, n}}_{n = 1}^{\infty}$ .

Nikitin, P.P. (2005)

Zapiski Nauchnykh Seminarov POMI

The representations and generic degrees of the Hecke algeba of type H4.

George Lusztig, Dean Alvis (1982)

Journal für die reine und angewandte Mathematik

The Residual Finiteness of Certain Amalgameted Free Products.

Martin Tretkoff (1973)

Mathematische Zeitschrift

The residually weakly primitive geometries of $J_{3}$ .

Leemans, Dimitri (2004)

Experimental Mathematics

The Restriction of a Representation of GL2(k) to GL2(o).

William Casselman (1973)

Mathematische Annalen

The Restriction of Admissible Representations to n.

William Casselman, M.Scott Osborne (1978)

Mathematische Annalen

The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces

Martin R. Bridson (2011)

Fundamenta Mathematicae

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.

Wolfgang Kühnel, Gunter Lassmann (1984/1985)

Manuscripta mathematica

The Ribes-Zalesskii property of some one relator groups

Gilbert Mantika, Narcisse Temate-Tangang, Daniel Tieudjo (2022)

Archivum Mathematicum

The profinite topology on any abstract group $G$ , 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 $G$ has the Ribes-Zalesskii property of rank $k$ , or is RZ $_{k}$ with $k$ a natural number, if any product $H_{1} H_{2} \dots H_{k}$ of finitely generated subgroups $H_{1}, H_{2}, \dots, H_{k}$ is closed in the profinite topology on $G$ . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ $_{k}$ for any natural number $k$ . In this paper we characterize groups...

The Riemann theorem and divergent permutations

Roman Wituła (1996)

Colloquium Mathematicae

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 $\sum a_{n}$ of real terms is rearranged by p to a divergent series $\sum a_{p (n)}$ . 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

Francesco Vaccarino (2005)

Annales de l’institut Fourier

We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring $R$ , 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].

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