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

SUBJECT

Code
Subject
MA263 Abelian Groups (2)
Section
Semester
Hours: C+S+L
Category
Type
Algebra and Geometry - in English
2
2+2+0
compulsory
Teaching Staff in Charge
Assoc.Prof. BREAZ Simion Sorin, Ph.D.,  bodomath.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D.,  calumath.ubbcluj.ro
Aims
Basic notions and results concerning divisibility, purity, basic subgroups and Ulm-Kaplansky invariants for abelian groups.
Content
Basic knowledges concerning divisibility (equivalence to injectivity, structure theorem), purity (the notion of purity in lattices, characterizations of purity for subgroups), basic subgroups (existence and uniqueness up to an isomorphism), Ulm-Kaplansky invariants and Ulm's theorem.
References
1. L. FUCHS: Infinite Abelian Groups, vol.1, Academic Press, 1970.
2. G. CALUGAREANU: Introducere laticiala in teoria grupurilor abeliene, Editura Expert, 1994.
3. G. CALUGAREANU, S. BREAZ, C. MODOI, C. PELEA, D. VALCAN: Exercises in abelian group theory, Kluwer Academic Publishers Group, Dordrecht, 2003
4. J.J. ROTMAN: An introduction to the theory of groups. Fourth edition. Springer-Verlag, New York, 1995.
5. J.L. ALPERIN, R.B. BELL: Groups and representations. Springer-Verlag, New York, 1995.
Assessment
Exam.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject