Amaglobeli, M. Exponential Groups III: Varieties of Groups (Stepennye gruppy III. Mnogoobraziya grupp). Preprint 5. Novosibirsk, 1993. In Russian.

Амаглобели, М. Г. Степенные группы III. Многообразия групп / Российская академия наук, Сибирское отделение, Институт математики ; рецензент доктор физико-математических наук А. Г. Мясников ; ответственный за выпуск доктор физико-математических наук Н. С. Романовский.
Новосибирск : ИМ СО РАН, 1993. 13 страниц. Препринт № 5.
Мягкая обложка. Обычный формат. Тираж 100 экземпляров. Первое издание.
Состояние: обложка хорошая, блок хороший, текст полный.
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Amaglobeli, M. G. Exponential Groups III: Varieties of Groups / Russian Academy of Sciences, Siberian Branch, Institute of Mathematics ; reviewed by A. G. Myasnikov, Doctor of Physical and Mathematical Sciences ; issued under the responsibility of N. S. Romanovsky, Doctor of Physical and Mathematical Sciences.
Novosibirsk : Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 1993. 13 pp. Preprint No. 5.
Paperback. Standard format. Print run of 100 copies. First edition.
Condition: wrapper good, text block good, text complete.

The third instalment of the founding sequence of papers on exponential (power) groups, and the point at which the series moved from Omsk to the Institute of Mathematics of the Siberian Branch in Novosibirsk, the flagship institute of the Soviet and Russian algebraic school. Continuing directly from the papers of Myasnikov and Remeslennikov and of Amaglobeli and Remeslennikov cited in its opening lines, the preprint turns to varieties of exponential A-groups and to tensor completions of groups within a variety, examining how the free groups of a given variety relate to one another under different rings of scalars. Amaglobeli describes the varieties of abelian A-groups in full, introduces several candidate analogues of the classical notion of an n-step nilpotent group within the category of A-groups, and proves that these analogues coincide for n equal to one and two; he further shows that the A-completion of a 2-step nilpotent group is itself 2-step nilpotent, a foundational closure result for the nilpotent theory later developed at length in Amaglobeli and Remeslennikov's work on free 2-step nilpotent R-groups. The preprint was reviewed by Alexei Myasnikov, co-founder of the theory, and issued under the editorial responsibility of Nikolai Romanovsky, himself a leading figure in the Novosibirsk school's work on algebraic geometry over groups and verbal subgroups. Printed in a run of only 100 copies on the Institute's own rotaprint, it is a scarce document of the theory's consolidation at its central Siberian institute and completes, together with the Omsk preprints Nos. 7, 9, and 11, a coherent four-part founding sequence in the history of exponential group theory.