Exercises in Abelian Group Theory (Texts in the Mathematical Sciences)

Valcan, D.; Pelea, C.; Modoi, C.; Breaz, S.; Calugareanu, Grigore

ISBN 10: 9048162491 / ISBN 13: 9789048162499

Editore: Springer, 2010

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Dati bibliografici

• Titolo: Exercises in Abelian Group Theory (Texts in the Mathematical Sciences)
• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048162491
• ISBN 13: 9789048162499
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

Preface. List of Symbols. I: Statements. 1. Basic notions. Direct sums. 2. Divisible groups. 3. Pure subgroups. Basic subgroup. 4. Topological groups. Linear topologies. 5. Algebraically compact groups. 6. Homological methods. 7. p-groups. 8. Torsion-free groups. 9. Mixed groups. 10. Subgroup lattices of groups. II: Solutions. 1. Basic notions. Direct sums. 2. Divisible groups. 3. Pure subgroups. Basic subgroups. 4. Topological groups. Linear topologies. 5. Algebraically compact groups. 6. Homological methods. 7. p-groups. 8. Torsion-free groups. 9. Mixed groups. 10. Subgroup lattices of groups. Bibliography. Index.