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

Code	Subject	
MML1001	Groups Theory and Applications	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics	1	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. COVACI Rodica, Ph.D., rcovaci@math.ubbcluj.ro	
Aims	Basic notions and results concerning general theory of groups, an introduction to the theory of group representations, some applications.	
Content	1. RUDIMENTS OF GROUP THEORY: Group, subgroup, index, Lagrange@s theorem, normal subgroup, factor group, homomorphisms, the isomorphism theorems, inner automorphisms, characteristic subgroups, center of a group, commutators, the derived group.
2. GROUP ACTIONS: Permutation groups, action of a group on a set, the associated representation, faithful actions, orbits and stabilizers, transitive actions, the orbit-stabilizer theorem, some applications.
3. LOCAL STRUCTURE OF FINITE GROUPS: Sylow@s theorems, Cauchy@s theorem, some applications.
4. NORMAL STRUCTURE OF GROUPS: Composition series, solvable groups, nilpotent groups.
5. GROUP REPRESENTATIONS: Schur@s lemma, Maschke@s theorem, characters.
6. APPLICATIONS OF GROUP THEORY: Applications in mathematics, applications in other fields.	
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. HUPPERT, B., Endliche Gruppen I, Springer-Verlag, Berlin - New York, 1967.
4. POPESCU, D.; VRACIU, C., Elemente de teoria grupurilor finite, Editura Stiintifica si Enciclopedica, Bucuresti, 1986.
5. PURDEA, I.; POP, I., Algebra, Editura GIL, Zalau, 2003.
6. PURDEA, I.; PELEA, C., Probleme de algebra, Editura EIKON, Cluj-Napoca, 2008.
7. ROTMAN, J.J., An Introduction to the Theory of Groups, Springer-Verlag, New York, 1995.	
Assessment	Report(50%) + Exam(50%).