## Around BurnsideThis is a truly encyclopaedic survey of the various aspects of the "restricted Burnside problem" and its surprising applications. Among many other things, it contains a detailed positive solution of the restricted Burnside problem for prime exponent, via Engel Lie algebras and so-called sandwiches. A new appendix to this translation contains a proof by E.I. Zel'manov of the existence of a recursive upper bound for the nilpotency class of a d-generator finite group of prime exponent p. Informative and illustrative comments grace the end of each chapter, and there is an extensive bibliography. |

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### Contents

Chapter | 1 |

Definitions and Examples | 4 |

The Locally Nilpotent Radical | 10 |

Copyright | |

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### Common terms and phrases

Adian Akad arbitrary arguments assertion associative algebra assume assumption automorphisms Burnside group Burnside problem Chap construction contains contradiction Corollary definition denote endomorphism Engel condition Engel Lie algebras English transl existence expression F of characteristic fact field F field of characteristic finite groups finite-dimensional formula free group free Lie algebra groups of exponent Higman induction Kostrikin Lemma Lie rings linear combination linear span locally nilpotent ideal locally nilpotent radical metabelian groups monomials multilinear natural number nil-element of index nilpotency class nilpotent ideal notation Notes Math obtained occurs p-groups pair of thin periodic groups permutation polynomial prime exponent Proc proof of Theorem properties Proposition 1.1 proved Remark restricted Burnside problem sandwich algebra sandwich Lie algebra sandwich of thickness satisfying the identity simple Lie algebra soluble subalgebra subgroup subsets summands Suppose Theorem 4.1 thin sandwiches Vaughan-Lee verbal ideal xS(p Zel'manov