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

Code	Subject	
MA262	Abelian Groups (1)	

Section	Semester	Hours: C+S+L	Category	Type	
Algebra and Geometry - in English	1	2+2+1		compulsory	

Teaching Staff in Charge	Assoc.Prof. COVACI Rodica, Ph.D., rcovaci@math.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D., calu@math.ubbcluj.ro	
Aims	Basic notions and results concerning general theory of groups and elements of the theory of group representations.	
Content	1. Rudiments of group theory: group, subgroup, normal subgroup, homomorphisms, the isomorphism theorems, permutation groups.
2. Automorphisms: the automorphism group of a group, inner automorphisms, characteristic subgroups, the derived group of a group.
3. Group actions, representations by permutations: action of a group on a set, the associated representation, faithful actions, orbits and stabilizers, transitive actions, the orbit-stabilizer theorem, some applications.
4. Local structure of finite groups: Sylow@s theorems, Cauchy@s theorem, applications.
5. Normal structure of groups: composition series, solvable groups, nilpotent groups.	
Bibliography	1. ALPERIN, J.L.; BELL, R.B., Groups and representations, Springer-Verlag, New York, 1995. 
2. BECHEANU, M., etc., Algebra, Editura ALL, Bucuresti, 1998.
3. CRIVEI, S., Basic abstract algebra, Casa Cartii de Stiinta, Cluj-Napoca, 2002.
4. HUPPERT, B., Endliche Gruppen I, Springer-Verlag, Berlin - New York, 1967.
5. PURDEA, I.; POP, I., Algebra, Editura GIL, Zalau, 2003.
6. ROTMAN, J., An Introduction to the Theory of Groups, Springer-Verlag, New York, 1995.
	
Assessment	Report(50%) + Exam(50%).