A comprehensive guide to ranks and group theory
Ranks of Groups features a logical, straightforward presentation,
beginning with a succinct discussion of the standard ranks before moving
on to specific aspects of ranks of groups. Topics covered include
section ranks, groups of finite 0-rank, minimax rank, special rank,
groups of finite section p-rank, groups having finite section p-rank for
all primes p, groups of finite bounded section rank, groups whose
abelian subgroups have finite rank, groups whose abelian subgroups have
bounded finite rank, finitely generated groups having finite rank,
residual properties of groups of finite rank, groups covered by normal
subgroups of bounded finite rank, and theorems of Schur and Baer.
This book presents fundamental concepts and notions related to the area
of ranks in groups. Class-tested worldwide by highly qualified authors
in the fields of abstract algebra and group theory, this book focuses on
critical concepts with the most interesting, striking, and central
results. In order to provide readers with the most useful techniques
related to the various different ranks in a group, the authors have
carefully examined hundreds of current research articles on group theory
authored by researchers around the world, providing an up-to-date,
comprehensive treatment of the subject.
- All material has been thoroughly vetted and class-tested by
well-known researchers who have worked in the area of rank conditions in
groups
- Topical coverage reflects the most modern, up-to-date research on
ranks of groups
- Features a unified point-of-view on the most important results in
ranks obtained using various methods so as to illustrate the role those
ranks play within group theory
- Focuses on the tools and methods concerning ranks necessary to
achieve significant progress in the study and clarification of the
structure of groups
Ranks of Groups: The Tools, Characteristics, and Restrictions is an
excellent textbook for graduate courses in mathematics, featuring
numerous exercises, whose solutions are provided. This book will be an
indispensable resource for mathematicians and researchers specializing
in group theory and abstract algebra.
MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics
at the University of Alabama.
LEONID A. KURDACHENKO, PhD, DrS, is Distinguished Professor and
Chair of the Department of Algebra at the University of Dnepropetrovsk,
Ukraine.
IGOR YA SUBBOTIN, PhD, is Professor in the Department of Mathematics
and Natural Sciences at National University in Los Angeles, California.
