Finite groups. An introduction. (Q2840674)

This textbook gives a smooth introduction to techniques on analysing the internal structure of finite groups. In Chapters I and II, being of an introductory nature, one finds topics also treated in other good textbooks, like: actions and permutations, commutators, automorphisms, (semi) direct products, normal sequences, nilpotent groups, (generalized) Fitting group, Frattini groups, automorphisms (including theorems of Schur, Gaschütz, Zassenhaus), \(p'\)-automorphisms of \(p\)-group, fixed points of automorphisms. In Chapter III topics from theorems on fusion and transfer are treated (including theorems of Glauberman and Thompson). In Chapter IV, results of Brauer and Fowler on involutions are presented. As special features here, one finds order formulas due to Bender. Finally, in Chapter V the reader encounters relatively short but very nice properties of linear groups, symplectic groups, orthogonal groups, unitary groups, Mathieu groups, the Higman-Sims group, the Chevalley groups and the Steinberg groups, Dynkin diagrams. There are a lot of illuminating exercises in the book. As an ``extra'', the reader will find 35 short curricula vitae of prominent group theorists; nice stuff!NEWLINENEWLINE The book is suited for use for master students in the first place and perhaps also for others. The reviewer welcomes the book as an addition to other well-known but more expanded texts. That is, this book offers to new-comers in the theory of finite groups, good, well-even and illuminating insights.