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Award ID contains: 1953784

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  1. ; (, Algebra and Logic)
    In this paper we describe generic elements and generic types in divisible rigid groups, in particular divisible free solvable groups. 
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  2. ; (, Izvestiya: Mathematics)
    In this paper we study the Diophantine problem in the classical matrix groups GL(n,R),SL(n,R),T(n,R),UT(n,R), n ≥ 3, over associative unitary rings R. We show that if G(n,R) is one of these groups then the Diophantine problem in G(n,R) is polynomial time equivalent (more precisely, Karp equivalent) to the Diophantine problem in R. Here for SL(n,R) we assume that R is commutative. Similar results hold for PGL(n,R) and PSL(n,R), provided R has no zero divisors (for PGL(n,R) the ring R is not assumed to be commutative). 
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