Around BurnsideSpringer Berlin Heidelberg, 27 sep. 1990 - 219 sidor Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator. It is most unusual, in a text of this type, in that the style is racy, with many literary allusions and witticisms: not the easiest to translate, but a source of inspiration to continue through material that could daunt by its combinatorial complexity. Moreover, there have been many changes to the text during the translating period, reflecting the ferment that the subject of the restricted Burnside problem is passing through at present. I concur with Professor Kostrikin's "Note in Proof', where he describes the book as fortunate. I would put it slightly differently: its appearance has surely been partly instrumental in inspiring much endeavour, including such things as the paper of A. I. Adian and A. A. Razborov producing the first published recursive upper bound for the order of the universal finite group B(d,p) of prime exponent (the English version contains a different treatment of this result, due to E. I. Zel'manov); M. R. Vaughan-Lee's new approach to the subject; and finally, the crowning achievement of Zel'manov in establishing RBP for all prime-power exponents, thereby (via the classification theorem for finite simple groups and Hall-Higman) settling it for all exponents. The book is encyclopaedic in its coverage of facts and problems on RBP, and will continue to have an important influence in the area. |
Innehåll
Chapter | 1 |
Definitions and Examples | 4 |
The Locally Nilpotent Radical | 10 |
Upphovsrätt | |
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a₁ abelian ideal Adian arbitrary arguments assertion associative algebra assume B₁ Burnside group Burnside problem c₁ c₁₂ c₁c₂ c₁u² c₂ c₂c₁ cc₁ Chap coc₁ commutators construction contains contradiction Corollary d₁ d₂ definition denote e₁ elements endomorphism Engel condition English transl existence expression F of characteristic fact field F field of characteristic finite groups finite-dimensional follows free group free Lie algebra groups of exponent i₁ induction j₁ k₁ Kostrikin L₁ Lemma Lie rings locally nilpotent ideal monomials multilinear natural number nilpotency class nilpotent ideal non-zero notation p-groups pair of thin periodic groups polynomial prime exponent Proc proof of Theorem properties proved relations sandwich algebra sandwich Lie algebra sandwich of thickness satisfying the identity simple Lie algebra soluble subalgebra subgroup subsets summands thick sandwich u₁ u₂ v₁ x₁ y₁ Zel'manov zero