ELEMENTARY THEORY OP FINITE GROUPS.

By Louis Clark Mathewson. Houghton Mifflin Company, 1930.

Professor Mathewson's book is the first really elementary text on the subject in the English language. Those who are aware of the significant role which the group concept plays in so many branches of mathematics will realize immediately what an important addition such a work must be to the library of the student or teacher of mathematics.

Beyond the introduction of the group concept and the study of numerous well-chosen examples, and the earlier work on permutation groups, somewhat of mathematical maturity is necessarily required of the reader. However, the author has done an excellent piece of work in presenting a rather technical subject with care and clarity. A few new theorems have been contributed to the subject, and new and simpler proofs have been furnished for a number of older theorems.

One of the outstanding features of the book is the series of carefully selected exercises, each set being graduated to include problems of varying degrees of difficulty; many of these are a real part of the development of the subject. Additional exercises refer the student to other works in the literature.

Surely Professor Mathewson has succeeded in making this text understandable, and it is to be expected that many mathematicians will give it the opportunity to prove itself teachable.