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By Hermann Stahl

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Kossuth University Debrecen, H:4010 Pf. Kossuth algebraic investigations in Hungary, University the Department and to report shortly on the in this department. It is an old cultural center. Debrecen is a small town The Kossuth Lajos University is one of the high schools of the town. The Department Number Theory belongs stitute to the five departments of the University. Algebraic of Algebra of Algebra and of the Mathematical investigations tion in the University. In this department worked Tibor Szele 1955) (1929-1974), and Andor Kert~sz In- have an old tradi(1918- both of them well known mathema- ticians.

Z I .... N. Latyshev, G. Genov, A. V. Yakovlev). role in Kemer's proof is played by the so called ~2- graded algebras A = A o + A I = (A,Ao,AI) where generally speaking A may not have a unit, and AoNA 1 ~ (0). I is spanned by all monomials of odd degree with respect to Z. ,AI) = 0. e. an ideal which is invariant under all graded endomorphisms T h e o r e m t (A,R. lem f o l l o w s ideal Kemer, 1984). T2(Mn(F),Mn(F ),Mn(F)) S u p p o s e now t h a t diction). , T2-ideals : T2(~) exist and an i n t e g e r is of Specht's the prob- graded false (and derive an i n f i n i t e a contra- chain of multilinear n > 1 such that T2 TZ(M n) ~ TZ(M n) + {f]} solution which contain f o r some n .

Algebra, 108 (]987), 116-126. "This paper is in final form and no version of it will be submitted for publication elsewhere" ON REPRESENTATIONS OF INFINITE GROUPS" K. Buzasl Mathematical Institute of L. Kossuth University Debrecen, H:4010 Pf. Kossuth algebraic investigations in Hungary, University the Department and to report shortly on the in this department. It is an old cultural center. Debrecen is a small town The Kossuth Lajos University is one of the high schools of the town. The Department Number Theory belongs stitute to the five departments of the University.

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