Structure Theory for Canonical Classes of Finite Groups

ISBN-13: 9783662516225 / Angielski / Miękka / 2016 / 359 str.

Wenbin Guo

Opis

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems."

Recenzje

"The book under review aims to be a continuation of these references and to analyze, systematize and report about subsequent developments in the theory of finite groups. ... A section at the end of each chapter includes additional related information and open problems. ... The book is addressed to people familiar with the theory of classes of groups and certainly of interest for researchers in this area of research." (M. Dolores Pérez-Ramos, Mathematical Reviews, June, 2016)

"The interested reader of this book is the specialist of general structure theory of groups, who will find a great number of results easily accessible in a unified presentation ready for deeper study, so far accessible only scattered in original research papers. ... The author boldly undertook and has successfully completed the task of presenting the diversified research methods and results, combining the application oriented approach with inviting exposition and pertinent examples." (János Kurdics, zbMATH 1343.20021, 2016)

Spis treści

The F-hypercentre and its generalizations.- Groups with given systems of X-permutable subgroups.- Between complement and supplement.- Groups with given maximal chains of subgroups.- Formations and Fitting classes