Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MML1001 | Groups Theory and Applications |
| 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. |
| References |
|
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%). |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |