Ebook: Exercises in Abelian Group Theory

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.

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This is the first book on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simple exercises (marked S1, S2 etc), of medium difficulty (M1, M2 etc) and ending with difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.

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This is the first book on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simple exercises (marked S1, S2 etc), of medium difficulty (M1, M2 etc) and ending with difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.
Content:
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

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This is the first book on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simple exercises (marked S1, S2 etc), of medium difficulty (M1, M2 etc) and ending with difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.
Content:
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
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