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By S. I. Adian (auth.), Jens L. Mennicke (eds.)

ISBN-10: 3540100067

ISBN-13: 9783540100065

ISBN-10: 3540381201

ISBN-13: 9783540381204

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Additional info for Burnside Groups: Proceedings of a Workshop Held at the University of Bielefeld, Germany June–July 1977

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B(m, n, ~+i) ~ ~ X a+l Y . 36 we Ba+ I of all e q u i v a l e n c e classes We denote this group by F(m, n, ~+i) . , p r e s e n t e d by the generators (16) and the A of r a n k i ~ ~+i . is infinite and has solvable w o r d problem. If we have proved for rank have b e e n used for rank some ~ + i . 5, p. 236). Now, as the r e s u l t of our induction, all our assertions have b e e n proved for a r b i t r a r y values of the p a r a m e t e r . Thus we can consider the set C l a s s i f i c a t i o n s of periodic words 33 co A: and the r e l a t i o n on n i:l R.

50 56 56 62 A finiteness p r o o f for F . . . . . . . . . . 124 A: The m a i n theorems . . . . . . . . . . . 125 B: The proofs . . . . . . . . . . . . . 131 Chapter 3: A d e s c r i p t i o n of G . . . . . . . . . . . 177 Chapter 4: A d e s c r i p t i o n of F . . . . . . . . . . . 182 References .. 187 .. . . . . . . . . . . . This is a report (finalized at this meeting) of the first steps in a study of groups of exponent 8 a i m e d at a n s w e r i n g the special case of B u r n s i d e ' s question: is every 2-generator group of exponent 8 finite?

If words W = fl[Wl; A transition pAtAIQ, P[A-I]n-t-IA21Q X A pAtAIQ , Y A P[A-1]n-t-iA2IQ r-reversal o f the occurrence in (22). a We shall call an arbitrary reversal of rank 2 . is can be found and the transition (22) is a simple X, pAtAIQ] . W ( Norm(2, X, 9) ( K1 X + Y C l a s s i f i c a t i o n s of periodic words We shall say that an o c c u r r e n c e of rank 2 if the o c c u r r e n c e (22). In this case if V2 flIV2; P[A-I]n-t-IA2IQ,Y]) is the image of VI in stable in the r e v e r s a l X + Y is stable in the simple r e v e r s a l in (22), then the o c c u r r e n c e image of is said to be thc V is X, pAtAIQ] VI = fl[V; This image of a stable o c c u r r e n c e X ÷ Y V in the reversal is u n i q u e l y defined.

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Burnside Groups: Proceedings of a Workshop Held at the University of Bielefeld, Germany June–July 1977 by S. I. Adian (auth.), Jens L. Mennicke (eds.)


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