Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II (Q1067006)

This is the second paper in a series devoted to algorithmic problems [for the first one see J. Pure Appl. Algebra 39, 53-94 (1986; Zbl 0577.20021)]. Here the authors use a variation of O. Kharlampovich's example of a finitely presented group of derived length 3 with insoluble word problem to derive some further results on algorithmic undecidability in soluble groups. They produce a recursive class of finitely presented groups of soluble length 3 with insoluble isomorphism problem. A recursive class of finitely presented groups of soluble length 3 or 4 is exhibited with no algorithm for determining the exact length of any of these groups. They also construct a class of soluble groups of derived length 3 where the problem of direct decomposability is insoluble. Finally they give an example of a finitely presented soluble group of derived length 3 where many properties of elements are insoluble.