Finitely generated metabelian and solvable groups.
Item
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Title
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Finitely generated metabelian and solvable groups.
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Identifier
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AAI3325464
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identifier
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3325464
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Creator
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Dean, Margaret H.
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Contributor
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Adviser: Gilbert Baumslag
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Date
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2008
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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The main results of this thesis are: (i) A wreath product of a free abelian group by a finitely generated torsion-free nilpotent group can be embedded in the skew field of fractions of the division ring of a nilpotent group; hence, a finitely generated free metabelian group can likewise be embedded. (ii) The free metabelian product of a free nilpotent group of class two and rank two with an infinite cyclic group is residually torsion-free nilpotent. (iii) The family of groups Gij = ⟨ a, b, c; a = [ci, a][c j, b]⟩, known to be absolutely parafree but not free, is relatively free in the variety of groups determined by the verbal subgroup [F", F']. (iv) Let P be parafree center by metabelian. Then H = P/P" is parafree in the variety of metabelian groups.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
