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

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

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J. Pure Appl. Math. 33, 230-238. FdM33,149. F. G. Kle~man] (1979), "Tom~eemsa M HeHOTOp61e anCODHTMHHeOHHe Npo6~eMbl S rpynnax" [Identities and some algorithmic problems in groups], Dokl. Akad. 818; Soviet Math. Dokl. 20, i15-i19. I. Adian Koypoec~a~ Tempa¢v. Hepe~e~e saCauu Teopuu ~pynn [Kourovka Notebook. Unsolved problems in the Theory of Groups] (4th Augmented edition) (Akad. Nauk SSSR Sibirsk. 0tdel. Inst. , Novosibirsk, 1973). MR51#I0443. A. A. Markov] (1946), "0 ~e3yc~osHO aaMKHyTSlX MHOmHCTBaX" [On unconditionally closed sets], Rec.

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. 4, 721-739 (1971). 20047; RZ [1971], PAl81. H. I. Adjan] (1976), "RepHOAHHeoHHe npoHaBeAeHH£ rpynn" [Periodical products of groups], ~ u d y Mat. Inst. Steklov. 142, 3-21. RZ [1977], 3A184. H. I~ Adian] (1978), "0 npoeToTe nepHoAHHecKHX npoHaHe~eHH~ rpynn", [On simple periodic products of groups], Dokl. Akad. Na~< SSSR 241, 745-748.

We have used a modification of our method to prove that such a group exists. d = da. An (i = i, 2 . . , m) = d An E U , , i=l where E. is a class of elementary words of the form elementary 9-power D of rank i related either with D or with D -I Clearly d . B(m, n) is the factor group of We prove that the group A(m, n) A(m, n) A(m, n) B(m, n) A n ~ E. that is by the subgroup generated by A(m, n) . is torsion free and every two non-identity have non-trivial intersection. 1 (7) this subgroup is the centre of subgroups of An A(m, n) also to prove that every finite is cyclic.

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