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Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers.
Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.
List of contents
Maximal subgroups and chief factors.- Classes of groups and their properties.- X-local formations.- Normalisers and prefrattini subgroups.- Subgroups of soluble type.- F-subnormality.- Fitting classes and injectors.
Summary
Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers.
Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.
Additional text
From the reviews:
"The authors of the book under review aim to collect what can be said in the same way about finite groups, soluble or not. … The book is very helpful for the reader to obtain information on recent results, a valuable source for anybody doing research in this area. … The style is similar to that of the series of ‘Ergebnisberichte’ with informative proofs and some direct references to the literature." (H. Heineken, Mathematical Reviews, Issue 2007 e)
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From the reviews:
"The authors of the book under review aim to collect what can be said in the same way about finite groups, soluble or not. ... The book is very helpful for the reader to obtain information on recent results, a valuable source for anybody doing research in this area. ... The style is similar to that of the series of 'Ergebnisberichte' with informative proofs and some direct references to the literature." (H. Heineken, Mathematical Reviews, Issue 2007 e)
