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2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.

A group theoretical model for mass-splitting

C. von Westenholz (1971)

Annales de l'I.H.P. Physique théorique

A Jones polynomial for braid-like isotopies of oriented links and its categorification.

Audoux, Benjamin, Fiedler, Thomas (2005)

Algebraic & Geometric Topology

A Kirillov theory for divisible nilpotent groups.

A.L. Carey, W. Moran, C.E.M. Pearce (1995)

Mathematische Annalen

A Lagrangian representation of tangles II

David Cimasoni, Vladimir Turaev (2006)

Fundamenta Mathematicae

The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.

A lantern lemma.

Margalit, Dan (2002)

Algebraic & Geometric Topology

A lattice of homomorphs

Paz Jiménez Seral (1993)

Rendiconti del Seminario Matematico della Università di Padova

A limit relation for Dunkl-Bessel functions of type A and B.

Rösler, Margit, Voit, Michael (2008)

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

A lower bound to the action dimension of a group.

Yoon, Sung Yil (2004)

Algebraic & Geometric Topology

A Magnus-Witt type isomorphism for non-free groups.

Ellis, G. (2002)

Georgian Mathematical Journal

A model for the universal space for proper actions of a hyperbolic group.

Meintrup, David, Schick, Thomas (2002)

The New York Journal of Mathematics [electronic only]

A natural framing of knots.

Greene, Michael, Wiest, Bert (1998)

Geometry & Topology

A new efficient presentation for $P S L (2, 5)$ and the structure of the groups $G (3, m, n)$

Bilal Vatansever, David M. Gill, Nuran Eren (2000)

Czechoslovak Mathematical Journal

$G (3, m, n)$ is the group presented by $〈 a, b ∣ a^{5} = {(a b)}^{2} = b^{m + 3} a^{- n} b^{m} a^{- n} = 1 〉$ . In this paper, we study the structure of $G (3, m, n)$ . We also give a new efficient presentation for the Projective Special Linear group $P S L (2, 5)$ and in particular we prove that $P S L (2, 5)$ is isomorphic to $G (3, m, n)$ under certain conditions.

A nilpotency condition for finitely generated soluble groups

Costantino Delizia (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that if $k > 1$ is an integer and $G$ is a finitely generated soluble group such that every infinite set of elements of $G$ contains a pair which generates a nilpotent subgroup of class at most $k$ , then $G$ is an extension of a finite group by a torsion-free $k$ -Engel group. As a corollary, there exists an integer $n$ , depending only on $k$ and the derived length of $G$ , such that $G / Z_{n} (G)$ is finite. For $k < 4$ , such $n$ depends only on $k$ .

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