Structure Theory for Canonical Classes of Finite Groups

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.

• Nilpotant groups
• Solvable groups
• Sylow subgroups
• X-permutable subgroups
• product of subgroups
• series and lattices of subgroups

“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)

• School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

  Wenbin Guo

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