## 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.

### MSC:

 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