MA262 | Abelian Groups (1) |
Teaching Staff in Charge |
Assoc.Prof. COVACI Rodica, Ph.D., rcovacimath.ubbcluj.ro Prof. CALUGAREANU Grigore, Ph.D., calumath.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. |
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. 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%). |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |