Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH422INTRODUCTION TO ABELIAN GROUPS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course With the help of the theoretical concepts of this course the students are expected to have knowledge and ability to classify abelian groups
Course Content Abelian goups. Quotient groups. Isomorphism theorems. Torsion part of the group. Decomposition of torsion groups into direct sum of primary groups. Divisibility. Injective groups. Structure of divisible groups. Projective groups. Free groups. Existence of epimorphisms from a projective groups and monomorphism into injective groups. Pure subgroups. Basic subgroups. Bounded pure subgroups. Classification of torsion-free groups of rank 1.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. ENGİN BÜYÜKAŞIK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Laszlo Fuchs, "Infinite abelian groups. Vol. I." Academic Press, New York-London 1970.
Irving Kaplansky, "Infinite abelian groups", University of Michigan Press, Ann Arbor, 1954.
Grigore Calugareanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Valcan,"Exercises in abelian group theory", Kluwer Texts in the Mathematical Sciences, 25. Kluwer Academic Publishers Group, Dordrecht, 2003.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Exams and Exam Preparations 1 124 124
Total Work Load   Number of ECTS Credits 5 160

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To use the isomorphism theorems.
2 To identify the structure of the torsion abelian groups.
3 To describe the properties of injective and projective groups.
4 To identify the importance of pure subgroups, basic subgroups and bounded pure subgroups.
5 To identify the classifications of rank 1 torsion free groups.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Preliminaries Laszlo Fuchs, "Infinite abelian groups. Vol. I."
2 Quotient groups. Isomorphism theorems. Direct Sums, Products. Finitely Generated Groups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
3 Torsion(free) abelian groups. Decomposition of torsion groups into direct sum of primary groups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
4 Divisibility. Injective groups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
5 Injective groups. Structure of divisible groups Laszlo Fuchs, "Infinite abelian groups. Vol. I."
6 Mid-term exam Laszlo Fuchs, "Infinite abelian groups. Vol. I."
7 Projective groups. Free groups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
8 Projective cover and injective envelope. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
9 Pure Subgroups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
10 Pure Subgroups .Bounded Pure Subgroups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
11 Mid-term exam Laszlo Fuchs, "Infinite abelian groups. Vol. I."
12 Basic Subgroups Laszlo Fuchs, "Infinite abelian groups. Vol. I."
13 Basic subgroups. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
14 Classification of torsion-free groups of rank 1. Laszlo Fuchs, "Infinite abelian groups. Vol. I."
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 3
C2 2 3
C3 0 3
C4 2 3 1
C5 2 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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