# Group Theory (dt. Gruppentheorie)

 Level, degree of commitment Advanced module, depends on importing study program Forms of teaching and learning,workload Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), recitation class (2 SWS), 180 hours (60 h attendance, 120 h private study) Credit points,formal requirements 6 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination (individual examination) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Subject, Origin Mathematics, B.Sc. Mathematics Duration,frequency One semester, Regularly alternating with other advanced modules Person in charge of the module's outline Prof. Dr. István Heckenberger

## Contents

• Matrix groups, permutation groups, symmetry groups
• Character theory of finite groups
• Group cohomology
• Extension theory of finite groups

## Qualification Goals

The students

• have gained insight into the beginnings of the theory of groups,
• understand abstract group structure as a source of symmetries,
• can transfer their skills with familiar groups such as numbers and matrices to more complex and abstract structures,
• can introduce and investigate new abstract structures based on simpler but still abstract structures,
• have developed mathematical ways of working (developing mathematical intuition and its formal justification, training in abstraction, reasoning),
• have improved their oral communication skills in lecture and tutorials by practicing free speech in front of an audience and in discussion.

## Prerequisites

None. The competences taught in the following modules are recommended: either Algebra [Bachelor Module] or Algebra [Lehramt Module].

• Huppert, B., Character Theory of Finite Groups, De Gruyter, 2011,
• Isaacs, M., Finite group theory, AMS, 2008

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

• Winter 2016/17 (no corresponding element)
• Summer 2018 (no corresponding element)
• Winter 2018/19 (no corresponding element)
• Winter 2019/20 (no corresponding element)
• Winter 2020/21 (no corresponding element)
• Summer 2021 (no corresponding element)
• Winter 2021/22 (no corresponding element)
• Winter 2022/23 (no corresponding element)
• Winter 2023/24

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.