First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
INTRODUCTION TO GROUP THEORY
SC03111814, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO GROUP THEORY
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge ANDREA LUCCHINI MAT/02

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC03111814 INTRODUCTION TO GROUP THEORY ANDREA LUCCHINI SC1172

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/02 Algebra 8.0

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Syllabus
Prerequisites: Basic knowedges in general algebra
Target skills and knowledge: We will give a general introduction to the theory of group, describing methods and results. In the second part of the course we will concentrate on particular topics (for example pro nite groups).
Examination methods: Oral. The candidate will be asked to present the most important arguments presented in the course, proving the more signi cant results and solving some related exercise.
Assessment criteria: Check of the learning of the taught notions and on the ability of their application.
Course unit contents: General introduction to group theory: actions of groups, solvable and nilpotent groups, fi nitely presented groups. A short history of the classi cation of finite simple groups. Topological groups, pro finite groups (characterizations, pro finite completion, countable based pro nite groups, arithmetical properties, subgroups of finite index in pro nite groups, Galois groups of in finite dimensional extension). Probabilistic methods in group theory.
Planned learning activities and teaching methods: Standar lectures at the blackboard, with exercises (solved in part by the students themseves).
Textbooks (and optional supplementary readings)
  • I.M. Isaacs, Finite group theory. Providence, Rhode Island: American Mathematical Society, 2008. Cerca nel catalogo
  • J. Wilson, Profinite groups. Oxford: Clarendon Press, 1998. Cerca nel catalogo