Exercises in Abelian Group Theory

✍ Scribed by Grigore Călugăreanu, Simion Breaz, Ciprian Modoi, Cosmin Pelea, Dumitru Vălcan (auth.)

• Publisher: Springer Netherlands
• Year: 2003
• Tongue: English
• Leaves: 353
• Series: Springer Texts in the Mathematical Sciences 25
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages N1-xii
Front Matter....Pages 1-1
Basic notions....Pages 3-19
Divisible groups....Pages 21-28
Pure subgroups....Pages 29-38
Topological groups....Pages 39-48
Algebraically compact groups....Pages 49-54
Homological methods....Pages 55-69
p -groups....Pages 71-83
Torsion-free groups....Pages 85-94
Mixed groups....Pages 95-104
Subgroup lattices of groups....Pages 105-110
Front Matter....Pages 111-111
Basic notions....Pages 113-142
Divisible groups....Pages 143-161
Pure subgroups....Pages 163-190
Topological groups....Pages 191-210
Algebraically compact groups....Pages 211-215
Homological methods....Pages 217-237
p -groups....Pages 239-260
Torsion-free groups....Pages 261-293
Mixed groups....Pages 295-317
Subgroup lattices of groups....Pages 319-332
Back Matter....Pages 333-351

✦ Subjects

Group Theory and Generalizations; Topological Groups, Lie Groups; Category Theory, Homological Algebra; Order, Lattices, Ordered Algebraic Structures