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.,  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