Presentations of groups.

*(English)*Zbl 0696.20027
London Mathematical Society Student Texts, 15. Cambridge etc.: Cambridge University Press. vii, 204 p. £9.95/pbk; $ 16.95/pbk (1990).

This is the third edition of a text that has clearly proved popular, based on lecture courses the author has given in England, Korea, and Australia. The first edition, with the same title, appeared in 1976 in the London Mathematical Society Lecture Note Series, No.22 [Zbl 0324.20040]; the second edition, entitled “Topics in the theory of group presentations”, appeared in 1980 in the same series, No.42 [Zbl 0437.20026]. The present text has several new chapters, on Nielsen’s Method, on relation modules, on an algorithm for the commutator factor group of a subgroup of finite index in a group given by a presentation, and on the nilpotent quotient algorithm. Several other chapters have been greatly revised. There are many examples and exercises. There are also a number of misprints, to keep the students alert and the misprint hunters (like this reviewer) happy. The author’s enthusiasm is obvious and adds to the attractiveness of the book.

Reviewer: B.H.Neumann