Exercises in Abelian Group Theory

1. Front Matter

   Pages N1-xii

   PDF

2. Statements

   1. Front Matter

      Pages 1-1

      PDF

   2. Basic notions

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 3-19

   3. Divisible groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 21-28

   4. Pure subgroups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 29-38

   5. Topological groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 39-48

   6. Algebraically compact groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 49-54

   7. Homological methods

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 55-69

   8. p-groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 71-83

   9. Torsion-free groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 85-94

   10. Mixed groups

       • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

       Pages 95-104

   11. Subgroup lattices of groups

       • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

       Pages 105-110

3. Solutions

   1. Front Matter

      Pages 111-111

      PDF

   2. Basic notions

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 113-142

   3. Divisible groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 143-161

   4. Pure subgroups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 163-190

   5. Topological groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 191-210

   6. Algebraically compact groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 211-215

   7. Homological methods

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 217-237

   8. p-groups

      • Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

      Pages 239-260

This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac­ ulty of Mathematics and Computer Science,'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992,these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu­ dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac­ ulty. The first draft of this collection, including only exercises solved by students as home works, the last ten years, had 160pages. We felt that there is a need for a book such as this one, because it would provide a nice bridge between introductory Abelian Group Theory and more advanced research problems. The book InfiniteAbelianGroups, published by LaszloFuchsin two volumes 1970 and 1973 willwithout doubt last as the most important guide for abelian group theorists. Many exercises are selected from this source but there are plenty of other bibliographical items (see the Bibliography) which were used in order to make up this collection. For some of the problems stated, recent developments are also given. Nevertheless, there are plenty of elementary results (the so called 'folklore') in Abelian Group Theory whichdo not appear in any written material. It is also one purpose of this book to complete this gap.

• Abelian group
• Group theory
• Lattice
• algebra
• topological group

• ‘Babeş Bolyai’ University, Cluj-Napoca, Romania

  Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan

• Kuwait University, State of Kuwait

  Grigore Călugăreanu

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