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	
MA262	Abelian Groups (1)	

Semester	Hours: C+S+L	Category	Status	
1	2+2+1		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
COVACI Rodica	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 general theory of groups and elements of the theory of group representations.	

IV. Course contents
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.	

V. 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.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Report(50%) + Exam(50%).	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. COVACI Rodica, Ph.D.