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The Burnside problem and identities in groups

Author: Sergej I Adjan
Publisher: Berlin [u.a.] : Springer, 1979.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 95.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Sergej I Adjan
ISBN: 3540087281 9783540087281 0387087281 9780387087283
OCLC Number: 263255677
Notes: Literaturverz. S. 303 - 308.
Description: x, 311 S.
Contents: I. Basic Concepts and Notation.- 1. Words and Occurrences.- 2. Periodic Words.- 3. Aperiodic Words.- 4. Inductive Definitions.- 5. Symmetry and Effectiveness.- II. Periodic and Elementary Words of Rank ?.- 1. Periodic Words of Rank ?.- 2. Integral Words and Generating Occurrences of Rank ?.- 3. Minimal and Elementary Periods of Rank ?.- 4. Periodisation.- 5. Elementary Words of Rank ?.- 6. Local Properties of Normalisability.- 7. Completely Regular Occurrences of Rank ? - 1 and Further.- Properties of Elementary Words.- III. Reversals of Rank ?.- 1. Elementary Properties of Reversals.- 2. Stable Occurrences and Local Reversals of Rank ?.- 3. Cascades and Real Reversals.- IV. Reduced Words and Equivalence in Rank ?.- 1. Kernels and Reduced Words of Rank ?.- 2. Equivalance in Rank ?.- 3. Mutually Normalised Occurrences.- V. Coupling in Rank ?.- 1. Properties of the Operation of "Coupling".- 2. Further Properties of Equivalent Words.- VI. Periodic Groups of Odd Exponent.- 1. Existence of Infinite Periodic Groups of Odd Exponent.- 2. Systems of Defining Relations for a Free Group of Finite Exponent.- 3. Subgroups of a Free Group of Finite Exponent.- VII. Further Applications of the Method.- 1. Non-Abelian Groups in which Every Pair of Cyclic Subgroups Intersect Non-Trivially.- 2. Infinite Independent Systems of Group Identities.- References.- Index of Notation.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, 95.
Other Titles: Problema Bernsajda i toždestva v gruppach.
Responsibility: S.I. Adian. Transl. from the Russian by John Lennox and James Wiegold.
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