Results 81 to 90 of about 5,391,081 (192)

Parabolic Subgroups of Artin Groups

Journal of Algebra, 1997
Let \((A,\Sigma)\) be an Artin system. For \(X\subseteq\Sigma\) by \(A_X\) is denoted the subgroup of \(A\) generated by \(X\). Such a group is called a parabolic subgroup of \(A\). Van der Lek's theorem is reproved: ``A parabolic subgroup of an Artin group is an Artin group''.
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Application of Group‐Theoretical Approaches in Structural Natural Frequency Analyses

International Journal for Numerical Methods in Engineering, Volume 127, Issue 7, 15 April 2026.
ABSTRACT Group theory has profoundly advanced physics and chemistry in systems with symmetries. Yet its use in structural engineering applications has not yet been fully explored beyond the aesthetics of symmetric designs. This work addresses two significant gaps that have limited the broader adoption of group‐theoretic methods in structural vibration ...
Shiyao Sun, Kapil Khandelwal
wiley   +1 more source

One-relator groups with torsion are conjugacy separable

, 2013
We prove that one-relator groups with torsion are hereditarily conjugacy separable. Our argument is based on a combination of recent results of Dani Wise and the first author.
Zalesskii, Pavel, Minasyan, Ashot
core   +1 more source

Normal points on Artin–Schreier curves over finite fields

Comptes Rendus. Mathématique
In 2022, S. D. Cohen and the two authors introduced and studied the concept of $(r, n)$-freeness on finite cyclic groups $G$ for suitable integers $r$, $n$, which is an arithmetic way of capturing elements of special forms that lie in the subgroups of $G$
Kapetanakis, Giorgos, Reis, Lucas
doaj   +1 more source

The Homological Algebra of Artin Groups.

MATHEMATICA SCANDINAVICA, 1994
The author's purpose is to give the foundations for a purely algebraic treatment of the homological algebra of Artin groups. The author gives algebraic proofs of the following theorems: Theorem A. Let \(G\) be an Artin group whose associated Coxeter group is finite. Then \(G\) is of type \(FL\). Theorem \(B\). Let \(G\) be as in Theorem A.
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Presentations of the braid group of the complex reflection group G(d,d,n)$G(d,d,n)$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We show that the braid group associated to the complex reflection group G(d,d,n)$G(d,d,n)$ is an index d$d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order d$d$. We also give a compatible presentation of G(d,d,n)$G(d,d,n)$ and its braid group for each tagged triangulation of the disk with ...
Francesca Fedele, Bethany Rose Marsh
wiley   +1 more source

Covers of D-Type Artin Groups

The Electronic Journal of Combinatorics, 2017
We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group $A(T)$ is defined by a signed graph $T$. Then we find a certain quotient $G(T)$ according to the graph $T$, which also have a natural map onto $A(D_n)$. We prove that $G(T)$ is isomorphic to a semidirect product of
Meirav Amram, Robert Shwartz, Mina Teicher   +2 more
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On the Structure and Homological Regularity of the q-Heisenberg Algebra

Axioms
The q-Heisenberg algebra hn(q) is a significant class of solvable polynomial algebras, and it unifies the canonical commutation relations of Heisenberg algebras and the deformation theory of quantum groups. In this paper, we employ Gröbner-Shirshov basis
Yabiao Wang, Gulshadam Yunus
doaj   +1 more source

Artin presentations, triangle groups, and 4-manifolds

, 2022
Gonzalez-Acuna showed that Artin presentations characterize closed, orientable 3-manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smooth, compact, simply connected 4-manifold.
Calcut, Jack S.
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Coherence of triangle artin groups [PDF]

, 2009
Artin groups have attracted a great deal of current research due to their strong connections to geometry. We investigate the relationship of Artin groups to 3-manifold groups and analyze the properties of their subgroups ...
Zhao, Junke
core   +1 more source