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This monograph presents both classical and recent results in the
theory of nilpotent groups and provides a self-contained,
comprehensive reference on the topic. While the theorems and proofs
included can be found throughout the existing literature, this is
the first book to collect them in a single volume. Details omitted
from the original sources, along with additional computations and
explanations, have been added to foster a stronger understanding of
the theory of nilpotent groups and the techniques commonly used to
study them. Topics discussed include collection processes, normal
forms and embeddings, isolators, extraction of roots,
P-localization, dimension subgroups and Lie algebras, decision
problems, and nilpotent groups of automorphisms. Requiring only a
strong undergraduate or beginning graduate background in algebra,
graduate students and researchers in mathematics will find The
Theory of Nilpotent Groups to be a valuable resource.
"Lectures on Finitely Generated Solvable Groups" are based on
the Topics in Group Theory" course focused on finitely generated
solvable groups that was given by Gilbert G. Baumslag at the
Graduate School and University Center of the City University of New
York. While knowledge about finitely generated nilpotent groups is
extensive, much less is known about the more general class of
solvable groups containing them. The study of finitely generated
solvable groups involves many different threads; thereforethese
notes contain discussions on HNN extensions; amalgamated and wreath
products; and other concepts from combinatorial group theory as
well as commutative algebra. Along with Baumslag s Embedding
Theorem for Finitely Generated Metabelian Groups, two theorems of
Bieri and Strebel are presented to provide a solid foundation for
understanding the fascinating class of finitely generated solvable
groups. Examples are also supplied, which help illuminate many of
the key concepts contained in the notes. Requiring only a modest
initial group theory background from graduate and post-graduate
students, these notes provide a field guide to the class of
finitely generated solvable groups froma combinatorial group theory
perspective. "
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