The Burnside Problem and Identities in Groups

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Table of 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.
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