Groups and representations. (English) Zbl 0839.20001

Alperin, J. L.; Bell, Rowen B.

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.

Reviewer: M.Deaconescu (Safat)

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

Keywords:

finite group theory; group actions; linear groups; local structure of finite groups; soluble groups; ordinary characters; Burnside’s \(p^ a q^ b\) theorem; first course