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Groups and representations. (English) Zbl 0839.20001
Graduate Texts in Mathematics. 162. New York, NY: Springer-Verlag. x, 194 p. (1995).
A concise text aimed to first year graduate students, this book covers the essentials of finite group theory: group actions and automorphisms, basic facts about linear groups, the normal and local structure of finite groups with a discussion of soluble groups, the ring-theoretic foundations of representation theory and ordinary characters, this last part culminating with a proof of Burnside’s \(p^a q^b\) theorem.
Elegant style and a good balance between theory and exercises blend together to provide a well suited text for a first course in finite group theory.

20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
20C15 Ordinary representations and characters
20Dxx Abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks