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135
Mathematics & Statistics
Ranks of Groups
The Tools, Characteristics, and Restrictions
Martyn R. Dixon, Leonid A. Kurdachenko & Igor Ya Subbotin
University of Alabama, USA; University of Dnepropetrovsk, Ukraine;
National University in Los Angeles, California, USA
ISBN: 978-1-119-08027-5 | Sep 2017 | 328PP
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.
About the Authors
Martyn R. Dixon, PhD, is Professor in the Department of Mathematics at the
University of Alabama.
Leonid A. Kurdachenko, PhD, 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.