"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Abelian groups
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MA262
1
2+1+1
8
compulsory
Algebră şi Geometrie - în limba engleză
Teaching Staff in Charge
Prof. CALUGAREANU Grigore, Ph.D.,  calumath.ubbcluj.ro
Assoc.Prof. COVACI Rodica, Ph.D.,  rcovacimath.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.