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The group of fractions of a semigroup S, if exists, can be written as G = SS−1. If S is abelian, then G must be abelian. We say that a semigroup identity is transferable if being satisfied in S it must be satisfied in G = SS−1. One of problems posed by G.Bergman in 1981 asks whether the group G must satisfy every semigroup identity which is satisfied in S, that is whether every semigroup identity...
We investigate the structure of groups satisfying apositive law, that is, an identity of the formu≡v, whereuandvare positive words. The main question here is whether all such groups are nilpotent-by-finite exponent. We answer this question affirmatively for a large class C of groups including soluble and residually finite groups, showing that moreover the nilpotency class and the finite exponent in...
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