Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>

Unit group of integral group ring <mml:math display="inline"><mml:mrow><mml:mi>ℤ</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>G</mml:mi> <mml:mo class="MathClass-bin">×</mml:mo> <mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>

Presenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3C3ℤ(S3×C3)(F55⋊F3)⋊(S3∗×C2)Fρρℤ(S3×C3)S3RS3R=ℤ[ω]ωℤ(G×C3)GV(G)GU(ℤ(G×C3))

Saved in:

Bibliographic Details
Main Author:	Ömer Küsmüş
Format:	Article
Language:	English
Published:	Miskolc University Press 2024-01-01
Series:	Miskolc Mathematical Notes
Online Access:	http://mat76.mat.uni-miskolc.hu/mnotes/article/4666
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

On <mml:math display="inline"><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mi>M</mml:mi><mml:mo class="MathClass-punc">,</mml:mo><mml:mi>P</mml:mi><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>-functions with some features and new inequalities
by: Erhan Set, et al.
Published: (2024-01-01)

General <mml:math display="inline"><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mo class="MathClass-open">(</mml:mo><mml:mi>k</mml:mi><mml:mo class="MathClass-punc">,</mml:mo><mml:mi>p</mml:mi><mml:mo class="MathClass-close">)</mml:mo><mml:mo class="MathClass-punc">,</mml:mo><mml:mi>ψ</mml:mi><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>-Hilfer fractional integrals
by: Bouharket Benaissa, et al.
Published: (2024-01-01)

Existence and blow up of solutions of a viscoelastic <mml:math display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo class="MathClass-open">(</mml:mo><mml:mi>x</mml:mi><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math>-biharmonic equation with logarithmic source term
by: Gülistan Butakın, et al.
Published: (2024-01-01)

Synthesis, Superoxide Dismutase Mimetic and Anticancer Activities of Metal Complexes of 2,2-Dimethylpentanedioic Acid(2<small.letters>dmepda</small.letters>H<mml:math> <mml:mrow> <mml:msub> <mml:mi></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math>) and 3,3-Dimethylpentanedioic acid(3<small.letters>dmepda</small.letters>H<mml:math> <mml:mrow> <mml:msub> <mml:mi></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math>): X-Ray Crystal Structures of [C<small.letters>u</small.letters>(3<small.letters>dmepda</small.letters>)(<small.letters>bipy</small.letters>)]<mml:math> <mml:mrow> <mml:msub> <mml:mi></mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>⋅</mml:mo><mml:msub> <mml:mrow> <mml:mtext>6H</mml:mtext> </mml:mrow> <mml:mtext>2</mml:mtext> </mml:msub> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:math> and [C<small.letters>u</small.letters>(2<small.letters>dmepda</small.letters>)(<small.letters>bipy</small.letters>)(E<small.letters>t</small.letters>OH)]<mml:math> <mml:mrow> <mml:msub> <mml:mi></mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>⋅</mml:mo><mml:mn>4</mml:mn><mml:mtext>EtOH</mml:mtext><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:mtext>bipy=</mml:mtext><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:msup> <mml:mn>2</mml:mn> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow></mml:mrow> </mml:mrow> </mml:math>Bipyridine)
Published: (2006-01-01)

Photoelectrochemical characterization and photocatalytic properties of mesoporous <mml:math alttext="${{{ext{TiO}}_{ext{2}} } mathord{left/ {vphantom {{{ext{TiO}}_{ext{2}} } {{ext{ZrO}}_2 }}} ight. kern- ulldelimiterspace} {{ext{ZrO}}_2 }}$"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>TiO</mml:mtext> </mml:mrow> <mml:mtext>2</mml:mtext> </mml:msub> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>ZrO</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> films
Published: (2006-01-01)

Aqueous photocatalytic oxidation of lignin and humic acids with supported <mml:math> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>TiO</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Published: (2006-01-01)

Theorem on the union of two topologically flat cells of codimension 1 in <mml:math> <mml:mrow> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math>
Published: (2006-01-01)

Existence of positive solutions for some polyharmonic nonlinear equations in <mml:math alttext="$mathbb{R}^{n}$"> <mml:mrow> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math>
Published: (2006-01-01)

Positively charged polysilsesquioxane/iodide lonic liquid as a quasi solid-state redox electrolyte for dye-sensitized photo electrochemical cells: infrared, <mml:math alttext="$^{{ext{29}}} {ext{Si}}$"> <mml:mrow> <mml:msup> <mml:mi></mml:mi> <mml:mrow> <mml:mtext>29</mml:mtext> </mml:mrow> </mml:msup> <mml:mtext>Si</mml:mtext> </mml:mrow> </mml:math> NMR, and electrical studies
Published: (2006-01-01)

Synthesis, Characterization, and Biotoxicity of <mml:math alttext="${fchem{N}hspace{-6.5pt} aisebox{9pt}{huge$frown$}hspace{-6.5pt}fchem{N}}$"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mtext>NN</mml:mtext> </mml:mrow> <mml:mo stretchy="true">⌢</mml:mo> </mml:mover> </mml:mrow> </mml:math> Donor Sulphonamide Imine Silicon(IV) Complexes
Published: (2006-01-01)

Effect of complexation with lanthanide metal ions on the photochromism of (1,3,3-trimethyl-<mml:math alttext="$5'$"> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>′</mml:mo> </mml:msup> </mml:math>-hydroxy-<mml:math alttext="$6'$"> <mml:msup> <mml:mn>6</mml:mn> <mml:mo>′</mml:mo> </mml:msup> </mml:math>-formyl- indoline-spiro2,2<mml:math alttext="$'$"> <mml:msup> <mml:mn></mml:mn> <mml:mo>′</mml:mo> </mml:msup> </mml:math>-[2h]chromene) in different media
Published: (2006-01-01)

On <mml:math display="inline"><mml:mi>n</mml:mi></mml:math>-derivations of generalized matrix algebras
by: Aisha Jabeen
Published: (2024-01-01)

<mml:math display="inline"><mml:mi>k</mml:mi></mml:math>-Srivastava hypergeometric functions and their integral representations
by: Sena Halıcı, et al.
Published: (2024-01-01)

An <mml:math alttext="$H$"> <mml:mi>H</mml:mi> </mml:math>-system for a revolution surface without boundary
Published: (2006-01-01)

On operators whose core–EP inverse is <mml:math display="inline"><mml:mi>n</mml:mi></mml:math>-potent
by: Dijana Mosić, et al.
Published: (2024-01-01)

On generalized <mml:math display="inline"><mml:mi>M</mml:mi></mml:math>-projective curvature tensor of para-Sasakian manifold
by: Swati Jain, et al.
Published: (2024-01-01)

The Auslander-Reiten correspondence about <mml:math display="inline"><mml:mi>∞</mml:mi></mml:math>-cotilting objects in extriangulated categories
by: Zhen Zhang, et al.
Published: (2024-01-01)

Nondecreasing bounded continuous solutions of a <mml:math display="inline"><mml:mi>q</mml:mi></mml:math>-difference equation
by: Hou Yu Zhao, et al.
Published: (2024-01-01)

On the local existence of solutions to <mml:math display="inline"><mml:mi>p</mml:mi></mml:math>-Laplacian equation with logarithmic nonlinearity and nonlinear damping term
by: Nazlı Irkıl
Published: (2024-01-01)

On two and three and four point boundary value problems for differential inclusions with <mml:math display="inline"><mml:mi>ϕ</mml:mi></mml:math>-Laplacian
by: Najib Askouraye, et al.
Published: (2024-01-01)

General existence principles for nonlocal boundary value problems with <mml:math alttext="$PHI$"> <mml:mi>φ</mml:mi> </mml:math>-laplacian and their applications
Published: (2006-01-01)

Bourgin-Yang-type theorem for <mml:math> <mml:mi>a</mml:mi> </mml:math>-compact perturbations of closed operators. Part I. The case of index theories with dimension property
Published: (2006-01-01)

Serum IL-1<mml:math alttext="$eta $"> <mml:mi>β</mml:mi> </mml:math>, IL-2, and IL-6 in Insulin-Dependent Diabetic Children
Published: (2006-01-01)

Solving Caputo fractional order differential equations via fixed point results of <mml:math display="inline"><mml:mi>α</mml:mi></mml:math>-Geraghty contraction type mappings
by: Abdellah Taqbibt, et al.
Published: (2024-01-01)

Some properties of <mml:math display="inline"><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle></mml:math>-supplemented modules
by: Celil Nebiyev, et al.
Published: (2024-01-01)

Circulating sCD138 and Some Angiogenesis-Involved Cytokines Help to Anticipate the Disease Progression of Early-Stage <mml:math><mml:mi>B</mml:mi></mml:math>-Cell Chronic Lymphocytic Leukemia
Published: (2006-01-01)

The Relationship Between Serum Levels of Total IgE, IL-18, IL-12, IFN-<mml:math> <mml:mi>γ</mml:mi> </mml:math> and Disease Severity in Children With Atopic Dermatitis
Published: (2006-01-01)

Elevated Circulating IL-1<mml:math> <mml:mi>β</mml:mi> </mml:math> and TNF-Alpha, and Unaltered IL-6 in First-Trimester Pregnancies Complicated by Threatened Abortion With an Adverse Outcome
Published: (2006-01-01)

TLR2 Expression in Relation to IL-6 and IL-1<mml:math alttext="$eta$"> <mml:mi>β</mml:mi> </mml:math> and their Natural Regulators Production by PMN and PBMC in Patients with Lyme Disease
Published: (2006-01-01)

PRESEE: An MDL/MML Algorithm to Time-Series Stream Segmenting
by: Kaikuo Xu, et al.
Published: (2013-01-01)

IFN-<inline-formula><math display="inline"><semantics><mrow><mo>τ</mo></mrow></semantics></math></inline-formula> Maintains Immune Tolerance by Promoting M2 Macrophage Polarization via Modulation of Bta-miR-30b-5p in Early Uterine Pregnancy in Dairy Cows
by: Xinyu Feng, et al.
Published: (2025-01-01)

Roadmap for Designing Donor-<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="bold-sans-serif">π</mi></mrow></semantics></math></inline-formula>-Acceptor Fluorophores in UV-Vis and NIR Regions: Synthesis, Optical Properties and Applications
by: Guliz Ersoy, et al.
Published: (2025-01-01)

On the Normalized Laplacian Spectrum of the Zero-Divisor Graph of the Commutative Ring <inline-formula><math display="inline"><semantics><msub><mstyle mathvariant="bold"><mi mathvariant="double-struck">Z</mi></mstyle><mrow><msubsup><mi mathvariant="bold-italic">p</mi><mn mathvariant="bold">1</mn><msub><mi mathvariant="bold-italic">T</mi><mn mathvariant="bold">1</mn></msub></msubsup><msubsup><mi mathvariant="bold-italic">p</mi><mn mathvariant="bold">2</mn><msub><mi mathvariant="bold-italic">T</mi><mn mathvariant="bold">2</mn></msub></msubsup></mrow></msub></semantics></math></inline-formula>
by: Ali Al Khabyah, et al.
Published: (2025-01-01)

Foundation Maths /
by: Croft, Anthony
Published: (2010)

Math 87 : an incremental development /
by: Hake, Stephen
Published: (1997)

Business Math Basics /
by: Swindle, Robert E.
Published: (1987)

Math Connections : a secondary mathematics core curriculum /
by: Berlinghoff, William P.
Published: (2006)

Saxon Math 6/5 /
by: Hake, Stephen
Published: (2004)

QALYs: The Math Doesn’t Work
by: Tia G. Sawhney, et al.
Published: (2023-07-01)

CDIO IDEOLOGY IN MATH TRAINING
by: Yuliya V. Vainshtein, et al.
Published: (2016-12-01)