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Maltsev bases and triangular representations of tensor products of Abelian groups. (English) Zbl 1230.20053

From the introduction: By constructing on an Abelian group \(A\) the Maltsev base, this group can be coordinated by means of vectors whose length is equal to some ordinal number \(\lambda\) that depends on \(A\). Furthermore, the Maltsev base enables us to construct a triangular representation of a group \(A\) by means of generating and defining relations. One part (Sections 1 and 2) of this paper is dedicated to the exposition of these ideas, while in the other part (Sections 3 and 4) the following problem is solved. Given two Abelian groups and their respective Maltsev bases and triangular representations, it is required to construct by this information a Maltsev base and a triangular representation for their tensor product. The results obtained in this paper are used to prove the theorems on nilpotent groups of nilpotency class \(\leq 3\). They are surely also helpful for generalizing these theorems to nilpotent groups whose nilpotency class is more than 3.

MSC:

20K35 Extensions of abelian groups
20F05 Generators, relations, and presentations of groups
20F18 Nilpotent groups
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