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Get Burnside Groups: Proceedings of a Workshop Held at the PDF

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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Read Online or Download Burnside Groups: Proceedings of a Workshop Held at the University of Bielefeld, Germany June–July 1977 PDF

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

Sample text

GI . n B. t ~ where T-I is a m i n i m a l period of rank : 2 . there are no involutions in the group i , All numbers k. must be odd b e c a u s e G . 7 there are some elementary words among these m i n i m a l periods of rank Ai consider all the e l e m e n t a r y periods b y adding all defining relations the group Ai GI of rank Let we define real reversals of rank 2 G2 ~==~X 2 in X : Y in of rank 2 to 2 , the sets G2 . X, f ( R 2 , f[ . We have also an algorithm w h i c h for an arbitrary word such that Ai X ~ Y .

2 generators such that any proper He also proved the existence of a two generator group of infinite order such thai any proper subgroup is cyclic of finite order. In the proof of these results he uses small cancellation theory and a similar classification of periodic words based on a simultaneous induction. H. I. Adjan] (1970), "GeCHOHeHHs;e HenpHsoAHmbJe CHCTeMSl FpynnoeblX TOH~eCT8" [Infinite irreducible systems of group identities], Izv. Akad. N a ~ SSSR Ser. Mat. 34, 715-734; Math. USSR-Izv.

Most of these results are contained in A d i a n (1979). 1. odd, The following properties of n ~ 665 B(m, n) hold true w h e n m ~ 2 and n is . 5). 13). 15). For a finitely g e n e r a t e d group d i f f e r e n t e l e m e n t s of G components that are the g e n e r a t o r s of we have the obvious e q u a t i o n natural number the group G let us denote b y w h i c h can be p r e s e n t e d G . 3 s-I . 16). 5). 2). 3). 4). 8). with countably many generators can be embedded in B(2, n) . The result (9) has been proved in ~irvanian It follows from (9) that the group maximal conditions for subgroups.

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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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