Abstract
A definition of the basis of a group written in additive form is given based on P. Hall's collecting process. The bases of free rank 2 groups of the following three types are found: metabelian, transmetabelian of the first type (with an Abelian third term in the lower central series), and transmetabelian of the second type (the nilpotency class of whose derived group is equal to two).
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References
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 126–139, 1991.
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Skopin, A.I. Bases of free metabelian and transmetabelian groups. J Math Sci 63, 684–692 (1993). https://doi.org/10.1007/BF01097983
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DOI: https://doi.org/10.1007/BF01097983