Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MA263	Abelian Groups (2)	

Section	Semester	Hours: C+S+L	Category	Type	
Algebra and Geometry - in English	2	2+2+0		compulsory	

Teaching Staff in Charge	Assoc.Prof. BREAZ Simion Sorin, Ph.D., bodo@math.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D., calu@math.ubbcluj.ro	
Aims	Basic notions and results concerning divisibility, purity, basic subgroups and Ulm-Kaplansky invariants for abelian groups.	
Content	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.	
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.
	
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.