Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Algebră şi Geometrie (în limba engleză)
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MA263	Abelian Groups (2)	

Semester	Hours: C+S+L	Category	Status	
2	2+2+0		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
BREAZ Simion Sorin	Ph.D.	Assoc.Prof.	Algebra	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Basic notions and results concerning divisibility, purity, basic subgroups and Ulm-Kaplansky invariants for abelian groups.	

IV. Course contents
Basic knowledges concerning divisibility (equivalence to injectivity, structure theorem), purity (the notion of purity in lattices, characterizations of purity for subgroups), basic subgroups (existence and uniqueness up to an isomorphism), Ulm-Kaplansky invariants and Ulm's theorem.	

V. Bibliography
1. L. FUCHS: Infinite Abelian Groups, vol.1, Academic Press, 1970. 
2. G. CALUGAREANU: Introducere laticiala in teoria grupurilor abeliene, Editura Expert, 1994.
3. G. CALUGAREANU, S. BREAZ, C. MODOI, C. PELEA, D. VALCAN: Exercises in abelian group theory, Kluwer Academic Publishers Group, Dordrecht, 2003
4. J.J. ROTMAN: An introduction to the theory of groups. Fourth edition.  Springer-Verlag, New York, 1995.
5. J.L. ALPERIN, R.B. BELL: Groups and representations. Springer-Verlag, New York, 1995.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
A written final exam (grade E), a test at the seminar (grade T) and a referee (R). The exam subjects have theoretical questions from all the studied topics, and one problem, among the problems studied at the course and last 4 seminars. The test subject have
practical questions (exercices and problems) from topics which are studied in first 10 weeks. The final grade is the weighted mean of the three grades mentioned above, conditioned by all the grades being at least 5 from 10. Otherwise, the exam will not be passed.
The final grade = 50%E + 25%T + 25%R. 	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. BREAZ Simion Sorin, Ph.D.