# Linear Groups

## The Accent on Infinite Dimensionality

Martyn R. Dixon ; Leonid A. Kurdachenko ; Igor Ya. Subbotin

Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional
linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. Les mer

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The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory.

The hope is that this book can be part of a similar transition in the field of linear groups.

Features

This is the first book dedicated to infinite-dimensional linear groups

This is written for experts and graduate students specializing in algebra and parallel disciplines

This book discusses a very new theory and accumulates many important and useful results

Preface. Essential Toolbox. Irreducible Linear Groups. Linear Groups which are close to Irreducible. Central Dimension and
its Generalizations. Linear Groups Saturated with Subgroups of Finite Central Dimension. Covering by Finite Dimensional Subspaces.
Bibliography. Author Index. Symbol Index. Subject Index.

Martyn R. Dixon is a Professor of Mathematics at the University of Alabama. He did undergraduate work at the University of
Manchester and obtained his Ph. D. at the University of Warwick under the guidance of Dr. Stewart Stonehewer. His main interests
in group theory include ranks of groups, infinite dimensional linear groups, permutable subgroups and locally finite groups.
He has written five books and almost one hundred articles concerned with group theory. He has been a visiting professor at
various institutions including the University of Kentucky, Bucknell University, Universita degli Studi di Trento, the University
of Napoli, the University of Salerno, the University of Valencia and the University of Zarogoza.

Dr. Leonid A. Kurdachenko is a Distinguished Professor and Chair of the Department of Geometry and Algebra of Oles Honchar Dnipro National University. He is one of the most productive group theorists. His list of publications consists of more than 250 journal articles published in major mathematics journals in many countries around the globe. He is an author of more than a dozen of books published by such prestigious publishers as John Wiley and Sons (USA), Birkhauser (Swiss), Word Scientific (United Kingdom), and others. He served as an invited speaker and visiting professor in many international conferences and universities. His research activities were supported by several prestigious international grants.

Dr. Subbotin is a Professor and Academic Director of mathematics programs at Sanford National University, USA. His main area of research is algebra. His list of publications includes more than 140 articles in algebra published in major mathematics journals around the globe. He also authored more than 50 articles in mathematics education dedicated mostly to theoretical base of some topics of high school and college mathematics. Among his publications there are several books published by such major publishing companies as Wiley and Sons, WorldScientific, Birkhauser, and other. His research in algebra was supported by several international prestigious grants, including grants issued by FEDER funds from European Union, The National Research Committee of Spain and Aragon, Volkswagen Foundation (VolkswagenStiftung), and others.

Dr. Leonid A. Kurdachenko is a Distinguished Professor and Chair of the Department of Geometry and Algebra of Oles Honchar Dnipro National University. He is one of the most productive group theorists. His list of publications consists of more than 250 journal articles published in major mathematics journals in many countries around the globe. He is an author of more than a dozen of books published by such prestigious publishers as John Wiley and Sons (USA), Birkhauser (Swiss), Word Scientific (United Kingdom), and others. He served as an invited speaker and visiting professor in many international conferences and universities. His research activities were supported by several prestigious international grants.

Dr. Subbotin is a Professor and Academic Director of mathematics programs at Sanford National University, USA. His main area of research is algebra. His list of publications includes more than 140 articles in algebra published in major mathematics journals around the globe. He also authored more than 50 articles in mathematics education dedicated mostly to theoretical base of some topics of high school and college mathematics. Among his publications there are several books published by such major publishing companies as Wiley and Sons, WorldScientific, Birkhauser, and other. His research in algebra was supported by several international prestigious grants, including grants issued by FEDER funds from European Union, The National Research Committee of Spain and Aragon, Volkswagen Foundation (VolkswagenStiftung), and others.