Some algorithmic problems for relatively free groupsстатьяПеревод
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Аннотация:The paper contains the proof of the algorithmic unrecognizability for two properties of some relatively free soluble groups, as well as the proof of the lack in a certain sense of the recursive enumerability for one more property of such groups. It is also proved that the indecomposability in the class of soluble finitely based varieties of groups is unrecognizable. An example is given of a relatively free soluble group with solvable word problem and with unsolvable identity problem. A result is obtained involving truth-table degrees of the word problem for relatively free soluble groups.