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Some New Directions In Commutativity Degree Of Finite Groups: Recent Developments - Couverture souple

Nath, Rajat Kanti

 
9783846546574: Some New Directions In Commutativity Degree Of Finite Groups: Recent Developments
Couverture souple
ISBN 10 : 3846546577 ISBN 13 : 9783846546574
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

Classification of finite groups is a central problem in theory of groups. Even though finite abelian groups have been completely classified, a lot still remains to be done as far as non-abelian groups are concerned. People all over the world have used various types of invariants for classifying finite non-abelian groups. The commutativity degree of a finite group is one such invariant. It is the probability that two randomly chosen group elements commute. This book contains some new results on commutativity degree of finite groups. Several generalizations of the concept of commutativity degree are introduced and studied in this book. In particular, some characterizations of finite groups are obtained in terms of commutativity degree and generalized commutativity degrees. Some generalizations of a classical result of F. G. Frobenius regarding the number of solutions of a commutator equation in a finite group are also disscussed. The book begins with a brief recollection of a few definitions and well-known results from several relevant topics, which constitute the minimum prerequisites for the subsequent chapters, and ends with a discussion on some possible research problems.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Classification of finite groups is a central problem in theory of groups. Even though finite abelian groups have been completely classified, a lot still remains to be done as far as non-abelian groups are concerned. People all over the world have used various types of invariants for classifying finite non-abelian groups. The commutativity degree of a finite group is one such invariant. It is the probability that two randomly chosen group elements commute. This book contains some new results on commutativity degree of finite groups. Several generalizations of the concept of commutativity degree are introduced and studied in this book. In particular, some characterizations of finite groups are obtained in terms of commutativity degree and generalized commutativity degrees. Some generalizations of a classical result of F. G. Frobenius regarding the number of solutions of a commutator equation in a finite group are also disscussed. The book begins with a brief recollection of a few definitions and well-known results from several relevant topics, which constitute the minimum prerequisites for the subsequent chapters, and ends with a discussion on some possible research problems.

Biographie de l'auteur

Rajat Kanti Nath received his M.Phil. and Ph.D. in Mathematics from North-Eastern Hill University under the supervision of Dr. A. K. Das. After spending sometime at Harish-Chandra Research Institute, Allahabad, as a Post-doctoral fellow he joined the faculty at Tezpur University, Assam. His research interests lie in the field of Group Theory.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3846546577
ISBN 13 
9783846546574
Reliure
Broché
Nombre de pages
156
Coordonnées du fabricant
non disponible
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