On the module of derivations of rings of invariants of k[X,Y ] under the action of certain dihedral groups

2021 ◽  
Author(s):  
Arindam Dey ◽  
Surjeet Kour
Keyword(s):  
Dihedral Groups ◽  
Linear Action ◽  
Generating Set

In this paper, we study the derivation module of the ring of invariants of [Formula: see text] under the linear action of dihedral groups [Formula: see text] mentioned in a paper by Riemenschneider [Die Invarianten der endlichen Untergruppen von [Formula: see text], Math. Zeitsch. 153 (1977) 37–50]. We obtained an explicit generating set for the derivation module of [Formula: see text]. We show that [Formula: see text].

scholarly journals Power graphs and exchange property for resolving sets

2019 ◽  
Vol 17 (1) ◽  
pp. 1303-1309 ◽  
Author(s):  
Ghulam Abbas ◽  
Usman Ali ◽  
Mobeen Munir ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Shin Min Kang
Keyword(s):  
Present Article ◽  
Linear Algebra ◽  
Finite Groups ◽  
Robot Navigation ◽  
Simple Graph ◽  
Exchange Property ◽  
Metric Dimension ◽  
Sufficient Condition ◽  
Resolving Set ◽  
Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

scholarly journals A generating set for the canonical ideal of HKG-curves

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Aristides Kontogeorgis ◽  
Ioannis Tsouknidas
Keyword(s):  
Generating Set ◽  
Canonical Ideal

Regular Cayley maps for dihedral groups

2021 ◽  
Vol 148 ◽  
pp. 84-124
Author(s):  
István Kovács ◽  
Young Soo Kwon
Keyword(s):  
Dihedral Groups ◽  
Cayley Maps

A Control System for a High-Quality Generating Set Equipped With a Two-Shaft Gas Turbine

1991 ◽  
Vol 113 (2) ◽  
pp. 290-295 ◽  
Author(s):  
H. Kumakura ◽  
T. Matsumura ◽  
E. Tsuruta ◽  
A. Watanabe
Keyword(s):  
Control System ◽  
Gas Turbine ◽  
Gas Turbines ◽  
High Quality ◽  
Constant Frequency ◽  
Generating Set ◽  
Generating Sets ◽  
Power Turbine ◽  
Computer Centers ◽  
Supply Systems

A control system has been developed for a high-quality generating set (150-kW) equipped with a two-shaft gas turbine featuring a variable power turbine nozzle. Because this generating set satisfies stringent frequency stability requirements, it can be employed as the direct electric power source for computer centers without using constant-voltage, constant-frequency power supply systems. Conventional generating sets of this kind have normally been powered by single-shaft gas turbines, which have a larger output shaft inertia than the two-shaft version. Good frequency characteristics have also been realized with the two-shaft gas turbine, which provides superior quick start ability and lower fuel consumption under partial loads.

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

scholarly journals On orbits of the automorphism group on an affine toric variety

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Ivan Arzhantsev ◽  
Ivan Bazhov
Keyword(s):  
Automorphism Group ◽  
Vector Space ◽  
Toric Variety ◽  
Connected Component ◽  
Linear Action

AbstractLet X be an affine toric variety. The total coordinates on X provide a canonical presentation $$\bar X \to X$$ of X as a quotient of a vector space $$\bar X$$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups

1992 ◽  
Vol 23 (2) ◽  
pp. 150
Author(s):  
David W. Jensen ◽  
Eric R. Bussian
Keyword(s):  
Theoretic Approach ◽  
Dihedral Groups

scholarly journals Intersection Conductance and Canonical Alternating Paths: Methods for General Finite Markov Chains

2014 ◽  
Vol 23 (4) ◽  
pp. 585-606
Author(s):  
RAVI MONTENEGRO
Keyword(s):  
Markov Chains ◽  
Cayley Graph ◽  
Mixing Time ◽  
Symmetric Case ◽  
Generating Set ◽  
Finite Markov Chains

We extend the conductance and canonical paths methods to the setting of general finite Markov chains, including non-reversible non-lazy walks. The new path method is used to show that a known bound for the mixing time of a lazy walk on a Cayley graph with a symmetric generating set also applies to the non-lazy non-symmetric case, often even when there is no holding probability.

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