Abelian groups

by Fuchs, László

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Title Statements

Full title :Abelian groups / by L. Fuchs.

Edition Statements

Publication Date:1967, ©1960
Edition:[3rd ed.]

Publication Statements

Publisher(s):Pergamon Press
Place of Publication:Oxford
Language:eng
Publication Date:1967, ©1960

The Physical Object

Description:1 online resource (367 pages)

Edition Identifiers

ISBN:9781483280905, 148328090X
oclc:ocn894772734
LC Classification:QA171
Dewey Decimal:512.86 UKW

Front Cover; Abelian Groups; Copyright Page; PREFACE; Table of Contents; TABLE OF NOTATIONS; CHAPTER I. BASIC CONCEPTS. THE MOST IMPORTANT GROUPS; 1. Notation and terminology; 2. Direct sums; 3. Cyclic groups; 4. Quasicyclic groups; 5. The additive group of the rationals; 6. The p-adic integers; 7. Operator modules; 8. Linear independence and rank; Exercises; CHAPTER II. DIRECT SUM OF CYCLIC GROUPS; 9. Free (abelian) groups; 10. Finite and finitely generated groups; 11. Direct sums of cyclic p-groups; 12. Subgroups of direct sums of cyclic groups; 13. Two dual criteria for the basis.

14. Further criteria for the existence of a basisExercises; CHAPTER III. DIVISIBLE GROUPS; 15. Divisibility by integers in groups; 16. Homomorphisms into divisible groups; 17. Systems of linear equations over divisible groups; 18. The direct summand property of divisible groups; 19. The structure theorem on divisible groups; 20. Embedding in divisible groups; Exercises; CHAPTER IV. DIRECT SUMMANDS AND PURE SUBGROUPS; 21. Direct summands; 22. Absolute direct summands; 23. Pure subgroups; 24. Bounded pure subgroups; 25. Factor groups with respect to pure subgroups.

26. Algebraically compact groups27. …