March 7, 2017

Burnside Groups: Proceedings of a Workshop Held at the by S. I. Adian (auth.), Jens L. Mennicke (eds.)

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

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

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Suppose that some of the periods rank 2 . 7 all such periods A. 9 3 . b e l o n g to R2 By Then we select the n. e l e m e n t a r y periods of rank defining relations for 3 from them. The c o r r e s p o n d i n g w o r d s Ai~ give the new G 3 , and so on. Obviously, after a finite number of steps, w e w i l l have e x h a u s t e d the set (i), o b t a i n i n g a group G. # w h i c h coincides with the o r i g i n a l group G . So the 45 Word problem for periodic relations solvability of the word problem of the group G is established.

Mennicke). that the nature of the subgroups of B(2, 8) B(m, n) is finite or not. This might suggest that a pointer to finiteness obtained if it were possible to show that subgroups. 41 of Robinson (1972)). Therefore infinite 2-groups have abelian subgroups of every context of groups of exponent generators. subgroups. B(2, 8) has comparatively discussed below. than that for For those with affirmative of B(2, 8) large finite Whatever one feels about such motivation, are more approachable In the these large finite abelian subgroups require many This suggests that a pointer to finiteness if one could show that which 8 2-power order.

2-generator group of exponent This has since been extended to class using the Canberra implementation of a related algorithm 12 called the 8 Groups of exponent eight nilpotent quotient algorithm (see Newman (1976)). studied the largest metabelian order 263 and nilpotency quotient group of class 12 51 Hermanns B(2, 8) (1977) has recently and has shown that it has (this has been confirmed by the nilpotent quotient algorithm). 8). Mennicke). that the nature of the subgroups of B(2, 8) B(m, n) is finite or not.

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