Abelian groups 
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Teaching Staff in Charge 
 

Aims 
Basic notions and results concerning divisibility, purity, basic subgroups and UlmKaplansky 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), UlmKaplansky 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. SpringerVerlag, New York, 1995. 5. J.L. ALPERIN, R.B. BELL: Groups and representations. SpringerVerlag, New York, 1995. 
Assessment 
Exam. 