Grupper og gruppeteori

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre- quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

About the first edition:"e;The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience."e; (Alberto Delgado, MathSciNet)"e;This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories."e; (Werner Kleinert, Zentralblatt)For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.Key Features are: - Provides an approach that minimizes advanced prerequisites; - Self-contained and systematic exposition requiring no previous exposure to Lie theory; -Advances quickly to the Peter-Weyl Theorem and its corresponding Fourier theory; - Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations - Exercises sprinkled throughout.This beginning graduate level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful.

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

This book gives a proof of Cherlin¿s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan¿s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin¿s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest toa wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.

Studienarbeit aus dem Jahr 2017 im Fachbereich Psychologie - Arbeit, Betrieb, Organisation, Note: 1, SRH Hochschule Riedlingen, Sprache: Deutsch, Abstract: Gruppen und Gruppenarbeit werden in Organisationen immer wichtiger. Vor allem in einer immer komplexer werdenden Welt ist es wichtig, das Wissen und die Fähigkeiten von Spezialisten in Gruppen zusammen zu führen, um auch die komplexesten Probleme lösen zu können. So passiert es nicht selten, dass Menschen aus verschiedensten Ländern, mit unterschiedlichen Kulturen an verschiedenen Standorten gemeinsam an einem Problem arbeiten. Bedingt durch die Megatrends Globalisierung und Digitalisierung ergeben sich also auch für die Einführung von Gruppenarbeit neue Herausforderungen.Im ersten Teil der Arbeit wird ein erster Überblick über das Thema ¿Gruppen- und Teamarbeit¿ sowie seine Relevanz verdeutlicht. Im zweiten Teil dieser Arbeit werden dann die theoretischen Grundlagen erläutert. Hierzu zählen einerseits die Merkmale von Gruppen und Arbeitsgruppen sowie die verschiedenen Formen von Gruppen- und Teamarbeit. Darüber hinaus werden die Vor- und Nachteile verdeutlicht und Optimierungsmöglichkeiten aufgezeigt. Im dritten Teil dieser Arbeit wird schließlich ein Vorgehensmodell zur Einführung von Gruppen- und Teamarbeit skizziert. Mit Kapitel vier folgt dann der Ausblick auf die Herausforderungen an die Gruppen- und Teamarbeit in einer digital vernetzten Arbeitsumgebung, bedingt durch die Industrie 4.0. Im fünften und letzten Kapitel folgt abschließend das Fazit des Autors.

Dieses Buch erleichtert Ihnen den Einstieg in das eigenstandige Losen von Aufgaben zur Algebra, indem es Ihnen nicht einfach nur Aufgaben mit Losungen, sondern vor allem auch Hinweise zur Losungsfindung und ausfuhrliche Motivationen bietet.Damit ist das Werk ideal geeignet zur Prufungsvorbereitung, wenn Sie ein tieferes Verstandnis der Algebra entwickeln wollen oder wenn Sie sich gerne an kniffligen Aufgaben einer faszinierenden mathematischen Disziplin versuchen.In den mehr als 300 Aufgaben unterschiedlicher Schwierigkeitsgrade durchleuchten wir die grundlegenden algebraischen Strukturen Gruppen, Ringe und Korper, wie sie typischerweise in einer Anfangervorlesung fur Mathematikstudierende behandelt werden.Vielfach berufen wir uns in den Losungen auf Satze, Lemmata und Korollare des Buches Algebra, Gruppen -Ringe - Korper von Ch. Karpfinger und K. Meyberg. Der AutorPD Dr. Christian Karpfinger lehrt an der Technischen Universitat Munchen; 2004 erhielt er den Landeslehrpreis des Freistaates Bayern.

History, Trauma and Shame provides an in-depth examination of the sustained dialogue about the past between children of Holocaust survivors and descendants of families whose parents were either directly or indirectly involved in Nazi crimes.

Originally published in 1981, this volume presents papers from the first Ontario Symposium on Personality and Social Psychology held at the University of Western Ontario from August 25-27, 1978. The general theme of the symposium was social cognition.

Bringing together trust research, rhetoric, ethnomethodology and conversation analysis, this book formulates an analytical program for conceptualizing and defining trustworthiness as an empirical research object in social interaction.Revisiting Trustworthiness in Social Interaction examines trustworthiness as a relational and dynamic concept. It reviews sociological and rhetorical approaches to the study of trustworthiness and respecifies it as an interactional phenomenon displayed, tested and negotiated by participants in social interaction. It identifies four participant orientations of trustworthiness that may be foregrounded in peoples' dynamic identity projects, and it defines the phenomena 'character-bound displays' and 'sequential negotiation of character', both indicative of participants' orientation to trustworthiness. In this way, the book turns the theoretical concept of trustworthiness into an empirical object of interaction analysis, pointing to a vast number of interactional indicators, which allow interaction analysts to explore if and how interactants orient to trustworthiness in an encounter. Exemplary cases from both mundane and institutional encounters are analyzed using ethnomethodological multimodal conversation analysis showing how trustworthiness is done, challenges, achived, negotiated and lost in interaction.The intended audiences are scholars of conversation analysis, ethnomethodology, rhetoric and the social sciences, especially communication, organizational and leadership studies, and their students.

This fascinating volume explores - from the perspective both of analysts and their patients-how the COVID-19 pandemic quickly and unexpectedly created profound and lasting changes in the ways psychoanalysis is conducted, and what those changes mean for analysis moving forward.The first part of the book is made up of interviews conducted by Stefano Carpani with authoritative authors in analytical psychology during the earliest phase of lockdown, centered on themes of the pandemic, lockdown, and how each individual was coping with the challenges those circumstances brought on. The second part features personal essays that further details the subjective experiences of Jungian analysts and therapists worldwide, comprising a collection of reflections on how COVID-19 affected and changed the way analysts work with patients. These reflections focus on the theoretical, clinical, technical, and also practical points of view, including clinical materials on transference and counter-transference considerations. The third part of the book is specular to the second and offers reflections from patients' perspective on how the pandemic changed their therapies and lockdown affected their experience of therapy. Patients have provided anonymous testimonies through their writing of how they experienced of the change of setting, mindset and related implications.A comprehensive overview of an important and ongoing conversation, Lockdown Therapy is crucial reading for Jungian analysts and scholars, as well as other clinicians training in analysis, psychotherapy and counselling.

This fascinating volume explores - from the perspective both of analysts and their patients-how the COVID-19 pandemic quickly and unexpectedly created profound and lasting changes in the ways psychoanalysis is conducted, and what those changes mean for analysis moving forward.

Presenting diverse perspectives from eminent scholars and contemporary researchers, The Handbook of Impression Formation contextualizes current and future areas of research in the social psychology of impression formation within a rich historic framework.Affirming that impression formation is at the core of human experience, chapters explore how and why people form snap judgments about others and when those impressions update. They examine the processes through which people infer the reasons for the events they encounter, allowing people to plan for appropriate behavioral responses to social contexts. The research reviewed is informed by the foundational theory of unconscious automatic processes involved in making judgements of other people, pioneered by Professor Jim Uleman who contributes a chapter that suggests important new directions, and concludes the volume by reflecting on the state of the field more broadly. The book explores how certain attributes stimulate categorization, examining current issues around implicit bias, stereotypes, and social media. Chapters cover a range of approaches, featuring personal narratives, presentation of new data and discoveries, comprehensive literature reviews, and contemplations on where the field must go and what questions require focus for progress to be made, calling for even the most advanced scholars to contribute more to the collective investigation of impression formation.This fascinating work provides a solid foundation from which all researchers can build a new and unique program of research, and arms the reader with the intellectual tools they need to chart new theoretical territory and discover aspects of the human experience we have yet to even wonder about. It is essential reading for students and academics in social psychology, and the social sciences more broadly.

Presenting diverse perspectives from eminent scholars and contemporary researchers, The Handbook of Impression Formation contextualizes current and future areas of research in the social psychology of impression formation within a rich historic framework.Affirming that impression formation is at the core of human experience, chapters explore how and why people form snap judgments about others and when those impressions update. They examine the processes through which people infer the reasons for the events they encounter, allowing people to plan for appropriate behavioral responses to social contexts. The research reviewed is informed by the foundational theory of unconscious automatic processes involved in making judgements of other people, pioneered by Professor Jim Uleman who contributes a chapter that suggests important new directions, and concludes the volume by reflecting on the state of the field more broadly. The book explores how certain attributes stimulate categorization, examining current issues around implicit bias, stereotypes, and social media. Chapters cover a range of approaches, featuring personal narratives, presentation of new data and discoveries, comprehensive literature reviews, and contemplations on where the field must go and what questions require focus for progress to be made, calling for even the most advanced scholars to contribute more to the collective investigation of impression formation.This fascinating work provides a solid foundation from which all researchers can build a new and unique program of research, and arms the reader with the intellectual tools they need to chart new theoretical territory and discover aspects of the human experience we have yet to even wonder about. It is essential reading for students and academics in social psychology, and the social sciences more broadly.

This ground-breaking volume presents a unique contribution to the development of social and political psychology both in Turkey and globally, providing a complex analysis of intergroup relations in the diverse Turkish context.